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Question 1 of 100
1. Question
1 pointsIf the sum of the two numbers is 120 and their quotient is 5. then the difference of the two numbers is…
Correct
\(Explanations\)
\(x+y=120…….(1)\)
\(\frac{x}{y} = 5\)
\(\Rightarrow x=5y\)
\(From Equation ….(1)\)
\(5y+5=120\)
\(\Rightarrow 6y=120\Rightarrow y=20\)
\(\therefore x=12020=100\)
\(\therefore\)Difference =10020=80Incorrect
\(Explanations\)
\(x+y=120…….(1)\)
\(\frac{x}{y} = 5\)
\(\Rightarrow x=5y\)
\(From Equation ….(1)\)
\(5y+5=120\)
\(\Rightarrow 6y=120\Rightarrow y=20\)
\(\therefore x=12020=100\)
\(\therefore\)Difference =10020=80 
Question 2 of 100
2. Question
1 pointsThe number of integers in between 100 and 600. which are divisible by 4 and 6 both. is
Correct
\(Explanation\)
We have to find such numbers which are divisible by 12. (LCM of 4 and 6).
Number of numbers divisible by 12 and lying between 1 to 600
\(=\frac{600}{12}1=49\)
Number of numbers by 12 from 1 to 100 \(=\frac{100}{12}=8\)
\(\therefore Required\) answer
\(=498=41\)Incorrect
\(Explanation\)
We have to find such numbers which are divisible by 12. (LCM of 4 and 6).
Number of numbers divisible by 12 and lying between 1 to 600
\(=\frac{600}{12}1=49\)
Number of numbers by 12 from 1 to 100 \(=\frac{100}{12}=8\)
\(\therefore Required\) answer
\(=498=41\) 
Question 3 of 100
3. Question
1 points(\(3^{25}+3^{26}+3^{27}+3^{28}\)) is divisible by
Correct
\(Explanation\)
\(3^{25}+3^{26}+3^{27}+3^{28}\)
\(=3^{25}(1+3+3^2+3^3)\)
\(=3^{25}(1+3+9+27)\)
\(=3^{25} \times 40, \)which is clearly divisible by 30.Incorrect
\(Explanation\)
\(3^{25}+3^{26}+3^{27}+3^{28}\)
\(=3^{25}(1+3+3^2+3^3)\)
\(=3^{25}(1+3+9+27)\)
\(=3^{25} \times 40, \)which is clearly divisible by 30. 
Question 4 of 100
4. Question
1 points\(\frac{1}{7}+(999\frac{692}{693})\times99\) is equal to
Correct
\(Explanation\)
\(\frac{1}{7}+(999+\frac{692}{693})\times 99\)
\(=\frac{1}{7}+999\times 99+\frac{692}{693}\times 99\)
\(=\frac{1}{7}+(10001)99+\frac{692}{7}\)
\(=\frac{1}{7}+\frac{692}{7}+9900099\)
\(\frac{693}{7}+9900099\)
\(=99+9900099=99000\)Incorrect
\(Explanation\)
\(\frac{1}{7}+(999+\frac{692}{693})\times 99\)
\(=\frac{1}{7}+999\times 99+\frac{692}{693}\times 99\)
\(=\frac{1}{7}+(10001)99+\frac{692}{7}\)
\(=\frac{1}{7}+\frac{692}{7}+9900099\)
\(\frac{693}{7}+9900099\)
\(=99+9900099=99000\) 
Question 5 of 100
5. Question
1 pointsIf 5432*7 is divisble by 9 then the digit in place of * is:
Correct
\(Explanation\)
A number is divisible by 9 if the sum of its digits is divisible by 9.
Let the number be \(x\)
\(\Rightarrow 5+4+3+2+x+7\)
\(=21+x\)
\(\therefore x=6\)
Incorrect
\(Explanation\)
A number is divisible by 9 if the sum of its digits is divisible by 9.
Let the number be \(x\)
\(\Rightarrow 5+4+3+2+x+7\)
\(=21+x\)
\(\therefore x=6\)

Question 6 of 100
6. Question
1 pointsIn a farm there are cows and hens. if heads are counted they are 180. if legs are counted they are 420. The number of cows in the farm is
Correct
\(Explanation\)
A cow and a hen each has a head
If the total number of cows be x, then
Number of hens\(=180x\)
A cow has four legs and a hen has two legs
\(\therefore (180x) \times 2+4x=420\)
\(\Rightarrow 3602x+4x=420\)
\(\Rightarrow 2x=420360=60\)
\(\Rightarrow x=\frac{60}{2}=30\)
Incorrect
\(Explanation\)
A cow and a hen each has a head
If the total number of cows be x, then
Number of hens\(=180x\)
A cow has four legs and a hen has two legs
\(\therefore (180x) \times 2+4x=420\)
\(\Rightarrow 3602x+4x=420\)
\(\Rightarrow 2x=420360=60\)
\(\Rightarrow x=\frac{60}{2}=30\)

Question 7 of 100
7. Question
1 pointsThe sum of two numbers is 75 and their difference is 25. the product of the two numbers is :
Correct
\(Explanation\)
Let the numbers be \(x\) and \(y\).
According to the question.
\(x+y=75\)
\(xy=25\)
\(\therefore (x+y)^2(xy)^2=4xy\)
\(\Rightarrow 75^225^2=4xy\)
\(\Rightarrow 4xy=(75+25)(7525)\)
\(\therefore a^2b^2=(a+b)(ab)\)
\(\Rightarrow 4xy=100\times 50\)
\(\Rightarrow xy=\frac{100\times50}{4}=1250\)
Incorrect
\(Explanation\)
Let the numbers be \(x\) and \(y\).
According to the question.
\(x+y=75\)
\(xy=25\)
\(\therefore (x+y)^2(xy)^2=4xy\)
\(\Rightarrow 75^225^2=4xy\)
\(\Rightarrow 4xy=(75+25)(7525)\)
\(\therefore a^2b^2=(a+b)(ab)\)
\(\Rightarrow 4xy=100\times 50\)
\(\Rightarrow xy=\frac{100\times50}{4}=1250\)

Question 8 of 100
8. Question
1 pointsthe sum of all natural numbers between 100 and 200. which are multiples of 3 is
Correct
\(Explanation\)
Numbers divisible by 3 and lying between 100 and 200 are 102, 105,……198
Let number of terms \(=n\)
\(\therefore 198=102+(n1)3\)
\(\Rightarrow n1=\frac{198102}{3}=32\)
\(\Rightarrow n=33\)
\(\therefore s=\frac{n}{2}=(a+l)\)
\(=\frac{32}{2}(102+198)=4950\)Incorrect
\(Explanation\)
Numbers divisible by 3 and lying between 100 and 200 are 102, 105,……198
Let number of terms \(=n\)
\(\therefore 198=102+(n1)3\)
\(\Rightarrow n1=\frac{198102}{3}=32\)
\(\Rightarrow n=33\)
\(\therefore s=\frac{n}{2}=(a+l)\)
\(=\frac{32}{2}(102+198)=4950\) 
Question 9 of 100
9. Question
1 pointswhat is the sum of two consecutive even numbers. the difference of whose square is 84 ?
Correct
\(Explanation\)
\((x+2)^2x^2=84\)
\(x^2+4x+xx^2=84\)
\(4x=844=80\)
\(x=\frac{80}{4}=20\)
\(\Rightarrow x+2=20+2=22\)
\(\therefore\)The required sum
\(=20+22=42\)Incorrect

Question 10 of 100
10. Question
1 pointsThe sum of three consecutive integers is 51. The middle one is :
Correct
\(Explanation\)
Let the numbers be \(x,x+1 and x+2\)
\(\therefore x+x+1x+x+2=51\)
\(\Rightarrow 3x+3=51\)
\(\Rightarrow 3x=513=48\)
\(\Rightarrow x=\frac{48}{3}=16\)
\(\therefore\) Middle number \(=16+1=17\)Incorrect
\(Explanation\)
Let the numbers be \(x,x+1 and x+2\)
\(\therefore x+x+1x+x+2=51\)
\(\Rightarrow 3x+3=51\)
\(\Rightarrow 3x=513=48\)
\(\Rightarrow x=\frac{48}{3}=16\)
\(\therefore\) Middle number \(=16+1=17\) 
Question 11 of 100
11. Question
1 pointsIf a number is as much greater than 31 as it is less than 75. then the number is
Correct
\(Explanation\)
If the numbers be \(x\)then
\(x31=75x\)
\(\Rightarrow 2x=75+31=106\)
\(\Rightarrow x=53\)Incorrect
\(Explanation\)
If the numbers be \(x\)then
\(x31=75x\)
\(\Rightarrow 2x=75+31=106\)
\(\Rightarrow x=53\) 
Question 12 of 100
12. Question
1 pointsA man traveled a distance of 80 km in 7 hr partly on foot at the rate of 8 km per hour and partly on bicycle at 16km per hour. The distance traveled on the foot is
Correct
\(Explanation\)
Journey on foot \(x \)km
Journey on cycle \(=(80x)\)km
\(\therefore \frac{x}{8}+\frac{80x}{16}=7\)
\(\Rightarrow \frac{2x+80x}{16}=7\)
\(\Rightarrow x+80=16\times7=112\)
\(x=12280=32 km\)
Incorrect
\(Explanation\)
Journey on foot \(x \)km
Journey on cycle \(=(80x)\)km
\(\therefore \frac{x}{8}+\frac{80x}{16}=7\)
\(\Rightarrow \frac{2x+80x}{16}=7\)
\(\Rightarrow x+80=16\times7=112\)
\(x=12280=32 km\)

Question 13 of 100
13. Question
1 pointsA car driver leaves Bangalore at 8.30 A.m and expects to reach a place 300 km from Bangalore at 12.30 P.M at 10.30 He finds that he has covered only 40% of the distance. By how much he has to increase the speed of the car in order to keep up his schedule
Correct
\(Explanation\)
Distance covered by car in 2 hours
\(=\frac{300\times40}{100}=120km\)
Remaining distance \(=300120=180 km\)
Remaining time \(=42\)
=2 hours
\(\therefore Required speed =\frac{180}{2}=90kmph\)
Original speed of car \(=\frac{120}{2}=60 kmph\)
\(\therefore \)Required increase in speed \(=9060=30 kmph\)
Incorrect
\(Explanation\)
Distance covered by car in 2 hours
\(=\frac{300\times40}{100}=120km\)
Remaining distance \(=300120=180 km\)
Remaining time \(=42\)
=2 hours
\(\therefore Required speed =\frac{180}{2}=90kmph\)
Original speed of car \(=\frac{120}{2}=60 kmph\)
\(\therefore \)Required increase in speed \(=9060=30 kmph\)

Question 14 of 100
14. Question
1 pointsA student goes to school at the rate of \(\frac{5}{2} \)km/hr. and reaches 6 minutes late. if the travels at the speed of 3km/hr. he reaches 10 minutes earlier. The distance of the school is
Correct
\(Explanation\)
Distance of school \(x\)km
Difference of time
\(16 min. = \frac{16}{60}hours\)
\(\therefore \frac{x}{\frac{5}{2}}\frac{x}{3}=\frac{16}{60}\)
\(\Rightarrow \frac{2x}{5}\frac{x}{3}=\frac{4}{15}\)
\(\Rightarrow \frac{6x5x}{15}=\frac{4}{15}\)
\(\Rightarrow \frac{x}{15}=\frac{4}{15}\)
\(\Rightarrow x=\frac{4}{15}\times 15=4km\)
Incorrect
\(Explanation\)
Distance of school \(x\)km
Difference of time
\(16 min. = \frac{16}{60}hours\)
\(\therefore \frac{x}{\frac{5}{2}}\frac{x}{3}=\frac{16}{60}\)
\(\Rightarrow \frac{2x}{5}\frac{x}{3}=\frac{4}{15}\)
\(\Rightarrow \frac{6x5x}{15}=\frac{4}{15}\)
\(\Rightarrow \frac{x}{15}=\frac{4}{15}\)
\(\Rightarrow x=\frac{4}{15}\times 15=4km\)

Question 15 of 100
15. Question
1 pointsA man travels for 5 hours 15 minutes. If he covers the first half of the journey at 60 km/hr. and rest at 45 km/hr. Find the total distance traveled by him.
Correct
\(Explanation\)
Let the distance covered be \(2x\)
\(Time=\frac{Distance}{speed}\)
According to the question
\(\frac{x}{60}+\frac{x}{45}=5\frac{15}{60}=5\frac{1}{4}\)
\(\Rightarrow \frac{3x+4x}{180}=\frac{21}{4}\)
\(\Rightarrow 7x=\frac{21}{4}\times 180\)
\(x=\frac{21\times 180}{4\times 7}=135 km\)
\(\therefore\) Length of total journey
\(=2\times 135=270 km\)
Incorrect
\(Explanation\)
Let the distance covered be \(2x\)
\(Time=\frac{Distance}{speed}\)
According to the question
\(\frac{x}{60}+\frac{x}{45}=5\frac{15}{60}=5\frac{1}{4}\)
\(\Rightarrow \frac{3x+4x}{180}=\frac{21}{4}\)
\(\Rightarrow 7x=\frac{21}{4}\times 180\)
\(x=\frac{21\times 180}{4\times 7}=135 km\)
\(\therefore\) Length of total journey
\(=2\times 135=270 km\)

Question 16 of 100
16. Question
1 pointsA train is running at a speed of 116 km\hr. The distance covered by the train in meters in 18 seconds is
Correct
\(Explanation\)
Speed of train \(=116 kmph\)
\(=(116\times\frac{5}{18})\frac{m}{sec.}\)
\(=(\frac{580}{18}) m/s\)
\(\therefore \)Required distance
\(=Speed \times Time\)
\(=(\frac{580}{18}\times 18)metre\)
\(=580 metre\)
Incorrect
\(Explanation\)
Speed of train \(=116 kmph\)
\(=(116\times\frac{5}{18})\frac{m}{sec.}\)
\(=(\frac{580}{18}) m/s\)
\(\therefore \)Required distance
\(=Speed \times Time\)
\(=(\frac{580}{18}\times 18)metre\)
\(=580 metre\)

Question 17 of 100
17. Question
1 pointsA man completes 30 km of a journey at the speed of 6 km/hr. and the remaining 40 km of the journey in 5 hours. His average speed for the whole journey
Correct
\(Explanation\)
Time taken to cover 30 km at \(60 kmph =\frac{30}{6}=5 hours\)
Time taken to cover \(40km=5 hours\)
\(\therefore Average speed\)
\(=\frac{Total Distance}{Total Time}=\frac{30+40}{10}\)
\(=\frac{70}{10}=7kmph\)
Incorrect
\(Explanation\)
Time taken to cover 30 km at \(60 kmph =\frac{30}{6}=5 hours\)
Time taken to cover \(40km=5 hours\)
\(\therefore Average speed\)
\(=\frac{Total Distance}{Total Time}=\frac{30+40}{10}\)
\(=\frac{70}{10}=7kmph\)

Question 18 of 100
18. Question
1 pointsA man covers the journey from a station A to station B at a uniform speed of 36 km/hr and returns to A with a uniform speed of 45 km/hr. His average speed for the whole journey is
Correct
\(Explanation\)
Here same distance are covered at different speeds.
\(\therefore \)Average speed
\((\frac{2xy}{x+y})kmph\)
\(=(\frac{2\times36\times45}{(36+45)})kmph\)
\(=\frac{2\times36\times45}{81}=40 kmph\)
Incorrect
\(Explanation\)
Here same distance are covered at different speeds.
\(\therefore \)Average speed
\((\frac{2xy}{x+y})kmph\)
\(=(\frac{2\times36\times45}{(36+45)})kmph\)
\(=\frac{2\times36\times45}{81}=40 kmph\)

Question 19 of 100
19. Question
1 pointsA train traveled at a speed of 35 km/hr for the first 10 minutes and at a speed of 20 km/hr for the next 5 minutes. The average speed of the train for the total 15 minutes
Correct
\(Explanation\)
Distance Covered
\(=(35\times \frac{10}{60}+20\times \frac{5}{60}\)
\(=(\frac{35}{6}+\frac{10}{6})=\frac{45}{6} km\)
Total time = 15 minutes
\(=\frac{1}{4} hour\)
\(\therefore \)Required average speed
\(=\frac{Distance covered}{Time taken}\)
\(=\frac{45}{6}\times 4\)
\(=30 kmph\)
Incorrect
\(Explanation\)
Distance Covered
\(=(35\times \frac{10}{60}+20\times \frac{5}{60}\)
\(=(\frac{35}{6}+\frac{10}{6})=\frac{45}{6} km\)
Total time = 15 minutes
\(=\frac{1}{4} hour\)
\(\therefore \)Required average speed
\(=\frac{Distance covered}{Time taken}\)
\(=\frac{45}{6}\times 4\)
\(=30 kmph\)

Question 20 of 100
20. Question
1 pointsThe ratio of length of two trains is 5:3 and the ratio of their speed is 6:5 The ratio of time speed is 6:5 The ratio time taken by them to cross a pole is
Correct
\(Explanation\)
Required ratio\(=\frac{5}{6}:\frac{3}{5}=\frac{30\times5}{6}:\frac{30\times 3}{5}\)
\(=25:18\)
Incorrect
\(Explanation\)
Required ratio\(=\frac{5}{6}:\frac{3}{5}=\frac{30\times5}{6}:\frac{30\times 3}{5}\)
\(=25:18\)

Question 21 of 100
21. Question
1 pointsA car travels 80 km in 2 hour and a train travels 180 km , in 3 hours the ratio of the speed of the car to that of the train is
Correct
\(Explanation\)
\(Speed=\frac{Distance}{Times}\)
\(\therefore\) Speed of car : Speed of train
\(=\frac{80}{2}:\frac{180}{3}=40:60=2:3\)
Incorrect
\(Explanation\)
\(Speed=\frac{Distance}{Times}\)
\(\therefore\) Speed of car : Speed of train
\(=\frac{80}{2}:\frac{180}{3}=40:60=2:3\)

Question 22 of 100
22. Question
1 pointsA student rides on bicycle at 8 km/hour and reaches his school 2.5 minutes late. The next day he increases his speed to 10 km/hr and reaches school 5 minutes early. How far is the school from his house ?
Correct
\(Explanation\)
Let \(x km\), be the required distance.
Difference in time
\(=2.5+5=7.5 minutes\)
\(=\frac{7.5}{60}hrs.=\frac{1}{8} hrs.\)
\(Now, \frac{x}{8}\frac{x}{10}=\frac{1}{8}\)
\(\Rightarrow \frac{5x4x}{40}=\frac{1}{8}\)
\(\Rightarrow x=\frac{40}{8}=5km\)
Incorrect
\(Explanation\)
Let \(x km\), be the required distance.
Difference in time
\(=2.5+5=7.5 minutes\)
\(=\frac{7.5}{60}hrs.=\frac{1}{8} hrs.\)
\(Now, \frac{x}{8}\frac{x}{10}=\frac{1}{8}\)
\(\Rightarrow \frac{5x4x}{40}=\frac{1}{8}\)
\(\Rightarrow x=\frac{40}{8}=5km\)

Question 23 of 100
23. Question
1 pointsA car can cover a certain distance in \(4\frac{1}{2} hours\). If the speed is increased by 5 km/hour. it would take \(\frac{1}{2}\) hour less to cover the same distance. Find the slower speed of the car
Correct
\(explanation\)
Let the initial speed of the car be \(x\) kmph and the distance by \(y\)km
Then \(y=\frac{9}{2}x…….(1)\)
\(and, y= 4(x+5)……….(2)\)
\(\therefore \frac{9x}{2}=4(x+5)\)
\(\Rightarrow 9x=8x+40\)
\(\Rightarrow x=40kmph\)
Incorrect
\(explanation\)
Let the initial speed of the car be \(x\) kmph and the distance by \(y\)km
Then \(y=\frac{9}{2}x…….(1)\)
\(and, y= 4(x+5)……….(2)\)
\(\therefore \frac{9x}{2}=4(x+5)\)
\(\Rightarrow 9x=8x+40\)
\(\Rightarrow x=40kmph\)

Question 24 of 100
24. Question
1 pointsA student goes to school at the rate of \(2\frac{1}{2}\) km/hr and reaches 6 minutes late. If he travels at the speed of 3km/h. he is 10 minutes early. The distance between the school and his house is
Correct
\(Explanation\)
Let the required distance be \(x\) km
\(\frac{x}{\frac{5}{2}}\frac{x}{3}=\frac{16}{60}\)
\(\Rightarrow \frac{2x}{5}\frac{x}{3}=\frac{4}{15}\)
\(\Rightarrow \frac{6x5x}{15}=\frac{4}{15}\Rightarrow x=4 km\)
Incorrect
\(Explanation\)
Let the required distance be \(x\) km
\(\frac{x}{\frac{5}{2}}\frac{x}{3}=\frac{16}{60}\)
\(\Rightarrow \frac{2x}{5}\frac{x}{3}=\frac{4}{15}\)
\(\Rightarrow \frac{6x5x}{15}=\frac{4}{15}\Rightarrow x=4 km\)

Question 25 of 100
25. Question
1 pointsTwo trains travel in the same direction at the speed of 56 kmph and 29 kmph respectively. The faster train passes a man in the slower train in 10 seconds. The length of the faster train (in metres) is
Correct
\(Explanation\)
Relative speed.
\(=5629=57 kmph\)
\(=27\times \frac{5}{18}=\frac{15}{2} m/sec\)
\(\therefore\) Distance covered in 10 seconds
\(=\frac{15}{2}\times10=75 m\)
Incorrect
\(Explanation\)
Relative speed.
\(=5629=57 kmph\)
\(=27\times \frac{5}{18}=\frac{15}{2} m/sec\)
\(\therefore\) Distance covered in 10 seconds
\(=\frac{15}{2}\times10=75 m\)

Question 26 of 100
26. Question
1 pointsA and B together can do a piece of work in 12 days. while B alone can finish it in 30 days. A lone can finish the work in ….
Correct
\(Explanation\)
Time taken by \(A=\frac{xy}{xy}\)
\(=\frac{12\times30}{3012}\)
\(=\frac{12\times30}{18}=20 days\)
Incorrect
\(Explanation\)
Time taken by \(A=\frac{xy}{xy}\)
\(=\frac{12\times30}{3012}\)
\(=\frac{12\times30}{18}=20 days\)

Question 27 of 100
27. Question
1 pointsA and B can do a piece of work in 36 days. B and C can do it in 60 days. A and C can do it in 45 days. C alone can do it in
Correct
\(Explanation\)
C alone can do in \(=\frac{2xyz}{xyyz+zx} days\)
\(=\frac{2\times36\times60\times45}{36\times6060\times45+45\times36}\)
\(=\frac{2\times36\times60\times3}{144180+108}\)
\(=\frac{72\times180}{252180}=180 days\)
Incorrect
\(Explanation\)
C alone can do in \(=\frac{2xyz}{xyyz+zx} days\)
\(=\frac{2\times36\times60\times45}{36\times6060\times45+45\times36}\)
\(=\frac{2\times36\times60\times3}{144180+108}\)
\(=\frac{72\times180}{252180}=180 days\)

Question 28 of 100
28. Question
1 pointsA can do a piece of work in 20 days and B can do the same piece of work in 30 days. Find in how many days both can do the work ?
Correct
\(Explanation\)
Time taken \(=\frac{xy}{x+y}\)
\(=\frac{20\times30}{20+30} days\)
\(=\frac{600}{50}=12 days\)
Incorrect
\(Explanation\)
Time taken \(=\frac{xy}{x+y}\)
\(=\frac{20\times30}{20+30} days\)
\(=\frac{600}{50}=12 days\)

Question 29 of 100
29. Question
1 pointsA and B can do a given piece of work in 8 days, B and C can do the same work in 12 days and A, B, C complete it in 6 days and Number of days required to finish the work by A and C is
Correct
\(Explanation\)
Let the time taken by A and C is \(x\)days
\(\Rightarrow 6=\frac{2\times x\times8\times12}{8x\times96+12x}\)
\(6=\frac{x\times192}{20x+96}\)
\(120x+576=192x\)
\(72x=576\)
\(x=8 days\)
Incorrect
\(Explanation\)
Let the time taken by A and C is \(x\)days
\(\Rightarrow 6=\frac{2\times x\times8\times12}{8x\times96+12x}\)
\(6=\frac{x\times192}{20x+96}\)
\(120x+576=192x\)
\(72x=576\)
\(x=8 days\)

Question 30 of 100
30. Question
1 pointsA and B can do a piece of work in 28 days 35 days respectively. They began to work together but a leaves after sometime and B completed remaining work in 17 days. After how many days did A leave ?
Correct
\(Explanation\)
Let A worked for \(x\)According to question
\(\frac{x}{28}+\frac{(x+17)}{35}=1\)
\(\Rightarrow \frac{5x+4(x+17)}{140}=1\)
\(\Rightarrow 5x+4x+68=140\)
\(\Rightarrow 9x=14068=72\)
\(\Rightarrow x=8\)
\(\therefore A \) worked for 8 days
Incorrect
\(Explanation\)
Let A worked for \(x\)According to question
\(\frac{x}{28}+\frac{(x+17)}{35}=1\)
\(\Rightarrow \frac{5x+4(x+17)}{140}=1\)
\(\Rightarrow 5x+4x+68=140\)
\(\Rightarrow 9x=14068=72\)
\(\Rightarrow x=8\)
\(\therefore A \) worked for 8 days

Question 31 of 100
31. Question
1 pointsA and B alone can complete work in 9 days and 18 days respectively.They worked together; however 3 days before the completion of the work A left. In how many days was the work A left. In how many days was the work completed ?
Correct
\(Explanation\)
Here, x=9, y=18, m=3
Total time taken
\(\frac{(x+m)\times18}{9+18}\)
\(\frac{12\times18}{27}=8 days\)
Incorrect
\(Explanation\)
Here, x=9, y=18, m=3
Total time taken
\(\frac{(x+m)\times18}{9+18}\)
\(\frac{12\times18}{27}=8 days\)

Question 32 of 100
32. Question
1 pointsIf 5 men or 7 women can earn RS.5,250 per day, how much would 7 men and 13 women earn per day ?
Correct
\(Explanation\)
5 men=7 women
( Both earn same amount in 1 days)
\(\therefore 7 men=\frac{7}{5}\times7=\frac{49}{5} women\)
\(\therefore 7 men+13 women\)
\(=\frac{49}{5}+13=\frac{114}{5} womem\)
Now,
\(\therefore 7 women=RS. 5,250\)
\(\therefore \frac{114}{5} women\)
\(=\frac{5250}{7}\times\frac{114}{5}=RS. 17,100\)
Incorrect
\(Explanation\)
5 men=7 women
( Both earn same amount in 1 days)
\(\therefore 7 men=\frac{7}{5}\times7=\frac{49}{5} women\)
\(\therefore 7 men+13 women\)
\(=\frac{49}{5}+13=\frac{114}{5} womem\)
Now,
\(\therefore 7 women=RS. 5,250\)
\(\therefore \frac{114}{5} women\)
\(=\frac{5250}{7}\times\frac{114}{5}=RS. 17,100\)

Question 33 of 100
33. Question
1 pointsStanie and Paul take a piece of work for RS.28,800. one alone could do it in 36 days. the other in 48 days. with the assistance of an expert. they finish it in 12 days. How much remuneration the expert should get ?
Correct
\(Explanation\)
Expert’s 1 day work \(=\frac{1}{12}\frac{1}{36}\frac{1}{48}\)
\(=\frac{1243}{144}=\frac{5}{144}\)
\(\therefore \)Ratio of their respective work for 1 day
\(=\frac{1}{36}:\frac{1}{48}\:\frac{5}{144}\:=4:3:5\)
\(\therefore\) Expert’s share
\(=\frac{5}{12}\times28800=RS.12000\)
Incorrect
\(Explanation\)
Expert’s 1 day work \(=\frac{1}{12}\frac{1}{36}\frac{1}{48}\)
\(=\frac{1243}{144}=\frac{5}{144}\)
\(\therefore \)Ratio of their respective work for 1 day
\(=\frac{1}{36}:\frac{1}{48}\:\frac{5}{144}\:=4:3:5\)
\(\therefore\) Expert’s share
\(=\frac{5}{12}\times28800=RS.12000\)

Question 34 of 100
34. Question
1 pointsA and B were assigned t0 do a job for an amount of RS.1,200. A alone can do it in 15 days. while B can do it in 12 days. with the help of C, The share of amount that C earns is
Correct
\(Explanation\)
According to the question
\(\frac{1}{15}+\frac{1}{12}+\frac{1}{C}=\frac{1}{5}\)
Let C’s work in day be \(\frac{1}{C}\)
\(\Rightarrow \frac{1}{C}=\frac{1}{5}\frac{1}{15}\frac{1}{12}\)
\(=\frac{1245}{60}=\frac{1}{20}\)
\(\therefore A:B:C=\frac{1}{15}:\frac{1}{12}:=\frac{1}{20}\)
\(=4:5:3\)
\(\therefore C’s\) Share
\(=\frac{3}{12}\times1200=RS.300\)
Incorrect
\(Explanation\)
According to the question
\(\frac{1}{15}+\frac{1}{12}+\frac{1}{C}=\frac{1}{5}\)
Let C’s work in day be \(\frac{1}{C}\)
\(\Rightarrow \frac{1}{C}=\frac{1}{5}\frac{1}{15}\frac{1}{12}\)
\(=\frac{1245}{60}=\frac{1}{20}\)
\(\therefore A:B:C=\frac{1}{15}:\frac{1}{12}:=\frac{1}{20}\)
\(=4:5:3\)
\(\therefore C’s\) Share
\(=\frac{3}{12}\times1200=RS.300\)

Question 35 of 100
35. Question
1 points2 men and 1 women together can complete a piece of work in 12 days. while 4 women and 2 men together can do it in in 8 days. if a man gets RS.600 per day. How much should a woman get per day ?
Correct
\(Explanation\)
According to the question, \((2\times14) men+14 women\)
\(= 16 men+32 women\)
\(\Rightarrow (2816) men\)
\(=(3214) women\)
\(\Rightarrow 12 men=18 women\)
\(\Rightarrow 2 men=3 women\)
\(\therefore 1 women=\frac{2}{3}man\)
\(\therefore \)Amount received by 1 woman
per day \(=\frac{2}{3}\times 600=RS.400\)
Incorrect
\(Explanation\)
According to the question, \((2\times14) men+14 women\)
\(= 16 men+32 women\)
\(\Rightarrow (2816) men\)
\(=(3214) women\)
\(\Rightarrow 12 men=18 women\)
\(\Rightarrow 2 men=3 women\)
\(\therefore 1 women=\frac{2}{3}man\)
\(\therefore \)Amount received by 1 woman
per day \(=\frac{2}{3}\times 600=RS.400\)

Question 36 of 100
36. Question
1 pointsA alone can complete a work in 10 days. B alone can do same work in 12 days and C alone can do the same work in 15 days. They jointly complete the work and earn RS.4500. what is the share of C
Correct
\(Explanation\)
Ratio of 1 day’s work of A, B and C \(=\frac{1}{10}:\frac{1}{12}:\frac{1}{15}\)
\(=\frac{1}{10}\times60:\frac{1}{12}\times60:\frac{1}{15}\times60\)
\([LCM of 10,12 and 15=60]\)
\(=6:5:4\)
Sum of the terms of ratio
\(=6+5+4=15\)
\(\therefore C’s\)Share
\(RS.(\frac{4}{15}\times4500)\)
\(=RS.1200\)
Incorrect
\(Explanation\)
Ratio of 1 day’s work of A, B and C \(=\frac{1}{10}:\frac{1}{12}:\frac{1}{15}\)
\(=\frac{1}{10}\times60:\frac{1}{12}\times60:\frac{1}{15}\times60\)
\([LCM of 10,12 and 15=60]\)
\(=6:5:4\)
Sum of the terms of ratio
\(=6+5+4=15\)
\(\therefore C’s\)Share
\(RS.(\frac{4}{15}\times4500)\)
\(=RS.1200\)

Question 37 of 100
37. Question
1 pointsP is four times as efficient. as Q. P can complete a work in 45 days less than Q. if both of them work together, then in how many days the work will be completed ?
Correct
\(Explanation\)
Time taken by P alone in doing work \(x\) days
\(\therefore 4x days\)
According to the question
\(\therefore 4xx=45\)
\(\therefore 3x=45\)
\(\therefore x=\frac{45}{3}=15days\)
\(\therefore \)Time taken by Q = 60 days
\(\therefore (P+Q)’s\) day’s work
\(=\frac{1}{15}+\frac{1}{60}=\frac{1+4}{60}\)
\(\frac{5}{60}=\frac{1}{12}\)
\(\therefore \)Required time = 12 days
Incorrect
\(Explanation\)
Time taken by P alone in doing work \(x\) days
\(\therefore 4x days\)
According to the question
\(\therefore 4xx=45\)
\(\therefore 3x=45\)
\(\therefore x=\frac{45}{3}=15days\)
\(\therefore \)Time taken by Q = 60 days
\(\therefore (P+Q)’s\) day’s work
\(=\frac{1}{15}+\frac{1}{60}=\frac{1+4}{60}\)
\(\frac{5}{60}=\frac{1}{12}\)
\(\therefore \)Required time = 12 days

Question 38 of 100
38. Question
1 pointsA work could be completed in 100 days by some workers. However. due to the absence of 10 workers. it was completed in 110 days. The original numbers of workers was .
Correct
Let the original number of workers \(x\)
then
\(x\times100=(x10)\times110\)
\(\Rightarrow 10x=11x110\)
\(\Rightarrow x=110\)
Incorrect
Let the original number of workers \(x\)
then
\(x\times100=(x10)\times110\)
\(\Rightarrow 10x=11x110\)
\(\Rightarrow x=110\)

Question 39 of 100
39. Question
1 pointsIf two persons. with equal abilities. can do two jobs in two days, then 100 persons with equal abilities can do 100 similar jobs in
Correct
\(Explanation\)
According to the question, 2 persons with equal abilities can do 1 job in 1 day
\(\therefore \)Time taken by 1 man to complete 1 job =2 days
\(\Rightarrow\) time taken by 100 persons in completing 100 jobs =2 days
Incorrect
\(Explanation\)
According to the question, 2 persons with equal abilities can do 1 job in 1 day
\(\therefore \)Time taken by 1 man to complete 1 job =2 days
\(\Rightarrow\) time taken by 100 persons in completing 100 jobs =2 days

Question 40 of 100
40. Question
1 pointsA can do a work in 12 days . When he had worked for 3 days. B joined him. If they complete the work in 3 more days. in how many days can B alone finish the work ?
Correct
\(Explanation\)
Let B alone do the work in \(x\) days
\(\therefore 6\times\frac{1}{12}+3\times\frac{1}{x}=1\)
\(\Rightarrow \frac{1}{2}+\frac{3}{x}=1\)
\(\Rightarrow \frac{3}{x}=\frac{1}{2}\Rightarrow x=6days\)
Incorrect
\(Explanation\)
Let B alone do the work in \(x\) days
\(\therefore 6\times\frac{1}{12}+3\times\frac{1}{x}=1\)
\(\Rightarrow \frac{1}{2}+\frac{3}{x}=1\)
\(\Rightarrow \frac{3}{x}=\frac{1}{2}\Rightarrow x=6days\)

Question 41 of 100
41. Question
1 pointsMatch the following
Set1 set2
a)Sun temple 1) Bhopal
b)Chitrakut 2) tamil nadu
c)Kanchipuram 3) konark
d)Sanchi Stupa 4) uttar pradesh
Correct
a3, b4, c2, d1
Incorrect
a3, b4, c2, d1

Question 42 of 100
42. Question
1 pointsChoose the correct options among the following
a)The headquarters of oil and natural gas is located at Dehradun
b)The Charminar is located at Hyderabad
c)The Indian school mines are located at Tatanagar
d)The central rice research institute is located at Cochin
Correct
a and b
Incorrect
a and b

Question 43 of 100
43. Question
1 pointsChoose the correctly matched pair among the following
a)Dilwara temples – Rajasthan
b)Golden temple – Amritsar
c)National institute of virology – Delhi
Correct
Incorrect
a and b

Question 44 of 100
44. Question
1 pointsThe holy place Badrinath is located on the bank of which of the rivers
Correct
Alaknanda
Incorrect
Alaknanda

Question 45 of 100
45. Question
1 pointsWhat are the number of metropolitan cities in India according to the 2011 survey
Correct
53
Incorrect
53

Question 46 of 100
46. Question
1 pointswhich of the following statement is incorrect
Correct
the percentage of population in India among the world is 10.04
reason: the percentage of population in india among world is 17.64
Incorrect
the percentage of population in India among the world is 10.04
reason: the percentage of population in india among world is 17.64

Question 47 of 100
47. Question
1 pointsChoose the incorrect statements among the following
1) The highest gender ratio is in Kerala (1084)
2) The least gender ratio is in Haryana (877)
3) The gender ratio in union territories is in Pondicherry (1038)
4) The gender ratio in union territories is in Daman and dui (618)
Correct
none of the above
Incorrect
none of the above

Question 48 of 100
48. Question
1 pointsWhat is the gender ratio in India
Correct
940
Incorrect
940

Question 49 of 100
49. Question
1 pointsAccording to census survey in 2011 what percent of families are provided with drinking water
Correct
85.5%
Incorrect
85.5%

Question 50 of 100
50. Question
1 pointsWhich of the following state is least developed in rail routes?
Correct
Manipur
Incorrect
Manipur

Question 51 of 100
51. Question
1 pointsWhich one is not correctly matched?
Correct
South Eastern Railway – Bhubaneswar
Incorrect
South Eastern Railway – Bhubaneswar

Question 52 of 100
52. Question
1 pointsWhich one of the following is the correct sequence of the given tiger reserves of India from north to south?
Correct
Dudwa – Kanha – Indravathi – Bandipur
Incorrect
Dudwa – Kanha – Indravathi – Bandipur

Question 53 of 100
53. Question
1 pointsWhich of the following state(s) have got largest forest cover in terms of percentage with respect to its geographical area?
Correct
Mizoram
Incorrect
Mizoram

Question 54 of 100
54. Question
1 pointsThe total forest area in India is around
Correct
63.72 million sq.km
Incorrect
63.72 million sq.km

Question 55 of 100
55. Question
1 pointsObserve these statements
1) Largest area of forest in India is Madhya Pradesh
2) Largest forest covered Union territory is Andaman Nicobar
3) Lease forest covered Union territory is Daman and Diu
4) Punjab state has least forest covered in India
Which of these statements are NOT correct?
Correct
All are correct
Incorrect
All are correct

Question 56 of 100
56. Question
1 pointsIndian Forest (Amendment) Ordinance, 2017 promulgated by President Ram Nath Kovind in Nov, 2017 and Amends Indian Forest Act, 2017.
The following statements are not correct
1) The bill omits Bamboo (taxonomically a grass) grown in nonforest areas from definition of trees
2) Encourage Bamboo plantation by farmers, which will contribute to doubling farmer’s income by 2032
Correct
2nd statement is not correct
Formers income will be doubled by 2022
Incorrect
2nd statement is not correct
Formers income will be doubled by 2022

Question 57 of 100
57. Question
1 pointsWhich of the following is Correct
Correct
All
Incorrect
All

Question 58 of 100
58. Question
1 pointsWhich of the following are true with respect to Indian Railways?
 It is the largest public sector undertaking
 Indian Ralway network is the fourth largest in the world
 Factories at Kapurthala and Perarnbur manufacture passenger coaches
 The narrow gauge lines are confined to the hilly areas only
Correct
1,2,34
Incorrect
1,2,34

Question 59 of 100
59. Question
1 pointsWhich of the following is the oldest atomic power station?
Correct
Tarapur
Incorrect
Tarapur

Question 60 of 100
60. Question
1 pointsWhich one of the following statement is NOT correct?
Correct
India ranks third in the world in coal production
Incorrect
India ranks third in the world in coal production

Question 61 of 100
61. Question
1 pointsWhich of the following is famous for Iron?
Correct
Kudremukh
Incorrect
Kudremukh

Question 62 of 100
62. Question
1 pointsAnkaleshwar and Navagaon are two oil fields in
Correct
Gujarat
Incorrect
Gujarat

Question 63 of 100
63. Question
1 pointsMatch the following
a. Nandadevi National park 1. Rajasthan
b.Keoladeo National Park 2.Assam
c.Manas Wildlife sanctuary 3. Gujarat
d.Gir National Park 4.Uttarakhand
Correct
a4, b1, c2, d3
Incorrect
a4, b1, c2, d3

Question 64 of 100
64. Question
1 pointsWhich of the following is not a UNESCO World Heritage Site?
Correct
None
Incorrect
None

Question 65 of 100
65. Question
1 pointsWhich Indian state has the longest coastline?
Correct
Gujarat
Incorrect
Gujarat

Question 66 of 100
66. Question
1 pointsThe Indian states which have common borders with Pakistan are?
Correct
Gujarat, jammu & Kashmir, Punjab, Rajasthan
Incorrect
Gujarat, jammu & Kashmir, Punjab, Rajasthan

Question 67 of 100
67. Question
1 pointsWhich of the following states has the max number of common borders with other Indian States?
Correct
Madhya Pradesh
Incorrect
Madhya Pradesh

Question 68 of 100
68. Question
1 pointsThe Indian rivers of the Indus basin are?
Correct
Sutlej , Beas, Ravi
Incorrect
Sutlej , Beas, Ravi

Question 69 of 100
69. Question
1 pointsWhat is the standard time of India with reference to Greenwich Mean Time?
Correct
5.30 hr fast
Incorrect
5.30 hr fast

Question 70 of 100
70. Question
1 pointsWhich statement is correct about The Himadri
a) This range is called Greater Himalayas
b) This is the highest mountain Range
c) It is average height is about 6100 meters
d) The world highest peaks like Mount Everest, Kanchujunga etc.,Correct
All are correct
Incorrect
All are correct

Question 71 of 100
71. Question
1 pointsWhich is the first National Park established in India?
Correct
Jim Corbett National Park
Incorrect
Jim Corbett National Park

Question 72 of 100
72. Question
1 pointsFrom where the Adam’s Bridge begins?
Correct
Dhanuskodi
Incorrect
Dhanuskodi

Question 73 of 100
73. Question
1 pointsWhich one of the following is the correct sequence of the age of formation of mountains from youngest to the oldest of the given mountain ranges?
Correct
Himalayas, Vindhyas, Westren Ghats, Deccan Traps
Incorrect
Himalayas, Vindhyas, Westren Ghats, Deccan Traps

Question 74 of 100
74. Question
1 pointsThe States which have common borders with China are:
 Jammu and Kashmir
 Sikkim
 Arunachal Pradesh
 Himachal Pradesh
Correct
1,2,3,4
Incorrect

Question 75 of 100
75. Question
1 pointsConsider the following
 Mahadeo Hills
 Sahyadri Parvat
 Satpura Hills
What is the correct sequence of the above from the north to the south?
Correct
1,3,2
Incorrect
1,3,2

Question 76 of 100
76. Question
1 pointsWest Bengal shares Boundaries with how many foreign
Correct
Three
Incorrect
Three

Question 77 of 100
77. Question
1 pointsAmong the Union Territories of India, which one has the largest size?
Correct
Puducherry
Incorrect
Puducherry

Question 78 of 100
78. Question
1 pointsIndia is divided into how many seismic zones to the earthquake zoning map
Correct
four
Incorrect
four

Question 79 of 100
79. Question
1 pointsWhich is the only Indian State that share its boundary with Sikkim
Correct
West Bengal
Incorrect
West Bengal

Question 80 of 100
80. Question
1 pointsIn which town, the Alaknanda and Bhagirathi rivers combine to form Ganga River
Correct
Devprayag
Incorrect
Devprayag

Question 81 of 100
81. Question
1 pointsWhich of the following longitudes determines the India Standard Time
Correct
82.5 Degree E
Incorrect
82.5 Degree E

Question 82 of 100
82. Question
1 pointsWhich Indian State shares longest international border
Correct
Rajasthan
Incorrect
Rajasthan

Question 83 of 100
83. Question
1 pointsTropic of Cancer passes through which of the Indian States:
Correct
Rajasthan, Jharkhand, West Bengal, Mizoram
Incorrect
Rajasthan, Jharkhand, West Bengal, Mizoram

Question 84 of 100
84. Question
1 pointsWhich of the following rivers are not correctly matched with their tributaries?
 Yamuna – Sind, Betwa, Ken
 Brahmaputra – Dibang, Lohit , Tista
 Narmada – Purna, Girna, Amravati
 Krishna – Pranhita, Musi, Sileru
Correct
3 and 4
Incorrect
3 and 4

Question 85 of 100
85. Question
1 pointsTumkur, where Geological Survey of India has found indications of Gold Reserves, is located in which among the following states?
Correct
Karnataka
Incorrect
Karnataka

Question 86 of 100
86. Question
1 pointsAt which among the following places, Brahamputra takes a Uturn at the time of entering into India?
Correct
Namcha Barwa
Incorrect
Namcha Barwa

Question 87 of 100
87. Question
1 pointsConsider the following:
 Burnpur in West Bengal
 Chandrapur in Maharastra
 Salem in Tamil Nadu
 Vijaynagar in Karnataka
For which of the following, the above are famous ?
Correct
Steel Plants
Incorrect
Steel Plants

Question 88 of 100
88. Question
1 pointsWhich among the following states leads in Handloom and Handicrafts clusters in India?
Correct
Uttar Pradesh
Incorrect
Uttar Pradesh

Question 89 of 100
89. Question
1 pointsWhich among the following rivers is known as Yarlung Tsangpo in Tibet?
Correct
Brahamputra
Incorrect
Brahamputra

Question 90 of 100
90. Question
1 pointsPrior to Census 2011, in which among the following census highest Sex Ratio was recorded in India?
Correct
Census 1961
Incorrect
Census 1961

Question 91 of 100
91. Question
1 pointsIn which of the following states, India’s maximum number of mines producing minerals (excluding minor minerals, petroleum (crude), natural gas and atomic minerals) are located?
Correct
Andhra Pradesh
Incorrect
Andhra Pradesh

Question 92 of 100
92. Question
1 pointsWhich among the following coal producer of India is outside the Coal India Ltd?
Correct
Singerani Collieries Company (Telangana)
Incorrect
Singerani Collieries Company (Telangana)

Question 93 of 100
93. Question
1 pointsIn which of the following states of India, there is no Petroleum Chemicals and Petrochemicals Investment Region (PCPIR)?
Correct
Assam
Incorrect
Assam

Question 94 of 100
94. Question
1 pointsThe K2 Peak is located in which of the following ranges?
Correct
Central Himalayas
Incorrect
Central Himalayas

Question 95 of 100
95. Question
1 points“Indira Gandhi super thermal power project “ is located in which state?
Correct
Haryana
Incorrect
Haryana

Question 96 of 100
96. Question
1 pointsWhich of the following Monsoons account for most of the rainfall in India?
Correct
South West Monsoon
Incorrect
South West Monsoon

Question 97 of 100
97. Question
1 pointsWhich among the following is the most optimum place to source Geothermal Energy?
Correct
Ladakh district
Incorrect
Ladakh district

Question 98 of 100
98. Question
1 pointsWhich among the following city is called “Zero Mile Center” because of its location on India’s Geographic center?
Correct
Nagpur
Incorrect
Nagpur

Question 99 of 100
99. Question
1 pointsConsider the following:
 Minor Irrigation Scheme: CCA less than 2000 Hectares
 Medium Irrigation Scheme : CCA more than 2000 Hectares but less than 10000 Hectares
 Major Irrigation Scheme : CCA more than 10000 Hectares
Which among the above statements is / are correct?
Correct
all are correct
Incorrect
all are correct

Question 100 of 100
100. Question
1 pointsIndira Col makes the 3point boundary between which of the following countries?
Correct
India, Pakistan, China
Incorrect
India, Pakistan, China
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