Problems on Trains - Aptitude Questions and Answers Part 2

6. Two boys are running in the same direction as that of the train. Their speeds are 8 km/hr and 16 km/hr respectively. The trains passes them fully in 40 seconds and 42 seconds respectively. Find the length of the train.

a. 180 m
b. 200 m    
c. 800 m
d. 1.8 km
                                                                                                                                                                                                                                  

Answer: d. 1.8 km

Explanation:

D = S x T
∴ S =D; T =D
TS


Let Speed of train be S km/hr.
Relative Speed of train for 1st boy = S - 8 km/hr
Relative Speed of train for 2nd boy = S - 16 km/hr
Distance covered = length of train = same for both
∴ D = D
∴ (S-8) x40= (S-16) x42----------- Divide by 60 x 60 to convert sec to hrs
60 x 6060 x 60
∴ S=176 km/hr
∴ Length of train = (S-8) x40= (176-8) x40= 1.8km = 1800m
60 x 6060 x 60


7. If a train stops on the way, its speed is 35 km/hr but if it doesn't, its speed is 40 km/hr. Find the number of minutes the train halts per hour.

a. 4 minutes
b. 6 minutes
c. 7.5 minutes
d. 8 minutes

Answer: c. 7.5 minutes

Explanation:

Difference in speed due to stopping = Speed without stoppage - Speed with stoppage
∴ Difference = 40-35 = 5km/hr
Thus, in 1 hour train covers 5 kms less.

Time taken to cover 4 km =5 km=1hrs. =1x 60 = 7.5 minutes
40 km/hr88


8. A bus is travelling from City A to City B. If the bus doesn't stop anywhere on the way, its average speed works out to 50 km/hr but if takes 4 stops of 15 minutes each, the average speed works out to 40 km/hr. Find the distance between the two cities.

a. 200 km
b. 360 km
c. 450 km
d. 630 km

Answer: c. 200 km

Explanation:

D = S x T
∴ S =D; T =D
TS


There are 4 stops of 15 min each. So total time spent in stops = 15 x 4 = 60 minutes = 1hour.
Let time taken without stopping be 'T' hours
So time with stopping = (T+1) hours
Distance is same   
∴ D = D
∴ S1 x T1 = S2 x T2
∴ 50 x T = 40 x (T+1)  
∴ T = 4 hours
Distance = 50 x 4 = 200 km.


9. A train starts at 8 pm from Station A towards Station B and travels at a speed of 40 km/hr. While another train starts at 9 pm in the opposite direction and travels at 60 km/hr. The two stations are 220 km apart. What will be the time by the watch when the two trains would meet?

a. 10:48 am
b. 10.08 pm
c. 10:48 pm
d. 11 pm

Answer: d. 10:48 pm

Explanation:

1st train (from A) travels 40 km in 1 hour i.e. from 8 pm to 9 pm
So when 2nd train starts at 9 pm, distance between the stations = 220-40 = 180 km
Since trains move in opposite direction, their relative speed= 40+60 = 100km/hr

Time taken to cover 180 km =180 km= 1.8 hours
100 km/hr
So they meet 1.8 hours after 2nd train starts i.e. 1.8 hours from 9 pm = 10:48 pm.


10. The distance between two stations is 240 km. When it strikes 5 pm in the clock, a train starts from each of these stations and travels towards the other one. They meet at a junction after 12 hrs. One of the trains is slower to the other one by 14km/hr. Find the speed of the slower train.

a. 3 km/hr
b. 5 km/hr
c. 7 km/hr
d. 13 km/hr

Answer: a. 3 km/hr

Explanation:

Let speed of slower train = S km/hr
Speed of faster = S+14
Trains meet after 12 hours.
Distance travelled by slower train in 12 hrs. = 12S
Distance travelled by faster train in 12 hrs. = 12(S+14)

The total distance to be traveled between the two stations is given.
So, 12S+12(S+14) = 240
2S + 14 = 20
S = 3 km/hr

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