Question 1
140 km
145 km
150 km
155 km
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Let the trains be A and B. A's speed = 60 Km/ h B's speed = 75 Km/ h At 10.30. the trains A and B are 30 Km apart.[ ½ travel of Train A] The relative speed of both trains is [7560 ] =15 Km/ h So to cover a distance of 30 Kms, they had to travel = 30/15 = 2 hours. Therefore the TWO TRAINS WILL MEET AT (10.30+2.00)= 12.30 P.M. The distance at which they will meet will be (75 x 2)= 150 Kms from KANPUR.
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Question 2
47
46
40
35
45
Fraction of work done by 28 children per day= 1/50
Fraction of work done by 1 child per day= 1/(50*28) equation(1)
Let x be the number of children needed to complete work in 30 days
Fraction of work done by x children in 1 day= 1/30
Fraction of work done by 1 child per day= 1/(30*x) equation(2)
consider equation (1 and 2)
50*28 = 30x
x= (50*28)/30
=> x=46.667 children
Question 3
6.12 kmph
6.42 kmph
6.22 kmph
6.32 kmph
Let the man from Delhi be A and that from Rohtak be B. After passing each other A takes 10/3 hrs to reach Rohtak. The speed of 8kmph. The distance from their meeting point to rohtak is : 10/3 × 8 = 80/3 km Let the total distance be x. The distance traveled by B to Delhi is : = (X  80/3) km Time = 16/3 hrs They took the same time to meet A having traveled (x  80/3)km and B having traveled 80/3 km Let speed of B be y (X  80/3)/8 = (80/3) / y Xy  80/3y = 640/3 y (x  80/3) = 640/3 Y = (640/3) / (x  80/3) The second face of the journey : A takes = (80/3) /8 hrs B takes = (x  80/3) / y = 16/3 = 3x  80 = 16y Substituting the value of y in this we have : 3x  80 = 16{(640/3)/(x  80/3) (3x  80)(x  80/3) = 10240/3 3x²  80x  80x + 6400/3 = 10240/3 3x²  160x + 6400/3 = 10240/3 3x²  160x  3840/3 = 0 3x²  160x  1280 = 0 We solve for x using quadratic formula : {160 +/ √(160² + 4 × 3 × 1280)} /2 × 3 {160 +/ 202.39} /6 x = 60.40 km Lets substitute this value in the following equation : 3x  80 = 16y We have : 3 × 60.4  80 = 16y 101.2 = 16y Y = 101.2/16 = 6.325 km/h
Question 4
24 days
21 days
18 days
15 days
As work is done by 28 men in 15 days at the rate of 6hr per day or, 28 men take 15×6 hr to finish the work. or, 28 men take 90 hr to finish the work. or, 1 man will take 90×28 hr to finish 1 work. or, amount of work done by 1 man in 1 hr = 1/2520 work no. of days =2520/21×8=2520/168= 15 days.
Question 5
50m
100m
150m
200m
Correct Answer : D Explanation: 200 m Speed = distance/time Distance= speed * time = (6045) * 48 * ( 5/18) ( relative speed in same direction is s1s2 and kmph to m/sec 5/18) = 200m
Question 6
18 m/s
16 m/s
20 m/s
14 m/s
Length of the Train = 240 m. Time taken by it to cross the Pole = 15 seconds. ∵ Speed = Distance or length of the train/Time ∴ Speed = 240/15 ⇒ Speed of the train = 16 m/s. Hence, the speed of the train is 16 m/s.
Question 7
120m
175m
Let length of platform = P m we know, distance = speed × time here, time = 1.5 × 60 sec = 90 sec speed = 54 × 5/18 = 15 m/s distance = (1200 + P) m 1200 + P = 15 × 90 1200 + P = 1350 P = 150 m hence, Length of platform = 150 m
Question 8
3.22 sec
4.98 sec
4.44 sec
4.22 sec
Since they are having same length, let. It be x.
Now, speed of Ist train=x/4.
Speed of 2nd train=x/5.
As per question, when moving in opposite direction, total length=x+x= 2x.
Total speed= (x/4)+(x/5)=(9x/20).
Time taken=(2x)÷(9x/20)=40/9=4.44 second
Question 9
Between 100 and 700
Less than 100
More than 900
More than 700
Correct Answer: A
Question 10
5 p.m.
4 a.m.
4 p.m.
5 a.m.
Correct Answer : C Explanation: With 60 kmph in 3 hours train, ‘A’ covers 180 km. Train B speed is 12kmph more than train ‘A’. Because train B started 3 hours later so it has to cover 180 extra with an extra 12kmph speed. Time taken is = 180/12 = 15 hours So 15 hours from 2p.m is 5a.m on the next day
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March 26, 2021
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