# SBI Clerk 2018: Quantitative Aptitude Quiz for Prelims – 23

Hello and welcome to exampundit. Here is a set of Quantitative Aptitude Quiz on Train based problems for Prelims exam of SBI Clerk 2018.

1. Two trains start at the same time from Mumbai and Pune and proceed towards each other at the rate of 56 km/h and 64 km/h respectively. When they meet it is found that the train has travelled 16 km more than the other. Find the distance between Mumbai and Pune?
(A) 250 km
(B) 240 km
(C) 230 km
(D) 220 km

Option: B

Explanation: Required distance=(Sum of the speeds/Difference of speeds)*Difference in distance
={(64+56)/(64-56)}*16=(120/8)*16=240km.

2. The distance between two stations Lucknow and Varanasi is 450km. A train starts from Lucknow and moves towards Varanasi at an average speed of 20 km/h. Another train starts from Varanasi,20 minutes earlier than the train at Lucknow,and moves towards Lucknow at an average speed of 30km/h. How far from Lucknow will the two trains meet?
(A) 176 km
(B) 186 km
(C) 196 km
(D) 166 km

Option: A

Explanation: Let the trains meet at a distance of x km from Lucknow.
(450-x/30)-(x/20)=20/60;
20(450-x)-30x/600=1/3;
9000-20x-30x=600/3;
9000-50x=200;
8800=50x;
X=8800/50=176km

3. The Maharaja Express leaves the station 1 hour before the scheduled time. The driver decreases its speed by 2km/h. At the next station 60km away,the train reached on time. Find the original speed of the Maharaja Express?
(A) 11km/h
(B) 14 km/h
(C) 12 km/h
(D) 13 km/h

Option: C

Explanation:

Let it takes x hours in second case
(60/x-1)-(60/x)=2,
(30/x-1)-(30/x)=1,
30x-30(x-1)=x^2-x
Or x^2-x-30=0;
X^2-6x+5x-30=0;
X(x-6)+5(x-6)=0
(x+5)(x-6)=0
X=-5,6

So original speed=60/5=12 km/h

4. Two trains of lenght 200m and 250m respectively with different speeds passes a static pole in 8 seconds and 14 seconds respectively. In what time will they cross each other when they are moving in same direction.
(A) 62 sec
(B) 64 sec
(C) 67 sec
(D) 63 sec

Option: D

Explanation: Speed of first train=200/8=25 m/s
Speed of second train=250/14=125/7 m/s
Total distance covered=200+250=450 m
Relative speed when they are moving in the same direction=25-125/7
Required time=450*7/50=63 sec

5. The speed of a train going from Kolkata to Burdwan is 100 km/h while its speed is 150 km/h when coming back from Burdwan to Kolkata. Then,the average speed during the whole journey is?
(A) 120km/h
(B) 125km/h
(C) 140km/h
(D) 135km/h

Option: A

Explanation: Lets use the formula of average speed=2xy/x+y
=2*100*150/100+150=120km/h

6. The speeds of Train C and Train D are in the ratio of 3:4. C takes 20 min more than D to reach a destination. Find time in which C reach the destination?
(A) 4/3h
(B) 2h
(C) 8/3h
(D) 5/3h

Option: A

Explanation:

Let the speed of C and D be 3x and 4x
According to the question
3x(t+20/60)=4x(t)
Or t=1h

Time for C to reach the destination=1+20/60=4/3h

7. A train covers a distance of 550m in 1 min whereas a metro train covers a distance of 33 km in 45 min. The ratio of their speeds is:
(A) 4:3
(B) 3:5
(C) 3:4
(D) 50:3

Option: C

Explanation: Speed of train=550*60/1000*1=33km/h
Speed of metro train=33/45*60=44km/h
Required Ratio=33/44=3:4

8. How many seconds will a 500m long train take to cross a man walking with a speed of 3km/h in the direction of the moving train,if the speed of the train is 63 km/h?
(A) 25
(B) 30
(C) 40
(D) 45

Option: B

Explanation: Relative speed of train wrt the person
=(63-3)*5/18 m/s=50/3 m/s
Time Taken=(500/50)*3=30 seconds

9. A train,100 m long,moving at a speed of 50km/h,crosses a train 120 m long coming from opposite direction in 6 seconds. The speed of the second train is?
(A) 82 km/hr
(B) 92 km/hr
(C) 77 km/hr
(D) 69 km/hr

Option: A

Explanation: When trains are moving in opposite directions,
Speed of the second train =Relative Speed- speed of the first train
={120+100/6 * 18/5}-50=132-50=82 km/hr

10. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m and travels towards B at 20 km/hr speed.Another train starts from B at 8 a.m and travels towards A at a speed of 25km/hr. At what time do they meet?
(A) 11 am
(B) 12 am
(C) 9 am
(D) 10 am

Option: D

Explanation: By Direct Formula we derive that ->
They will meet at 8 a.m + (110-(8 a.m-7 a.m)*20)/20+25
=8 a.m+2 hr=10 a.m

Regards

Team Exampundit

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