M4maths Previous Puzzles

12 Apr 2022 Time Distance & Speed

Train A whose length is four-fifth of that of train B crosses it travelling in opposite direction in a time which is 4/7 th of the time taken by train A to cross it when travelling in same direction. Calculate the ratio of the speeds of train A and train B.

OPtion

1) 4 : 5
2) 8 : 3
3) 3 : 7
4) 11 : 3
5) 1 : 3
6) 7 : 2
7) 12 : 5
8) 10 : 3
9) 9 : 2
10) None of these

Solution

Let lengths of trains B = x, then length of train A = (4/5)*x
Distance covered in each case =x + (4/5)*x = (9/5)*x
Let the speed of train A and train B be S1 and S2 respectively.
Relative speed in same direction = (S1-S2)
Relative speed in opposite direction = (S1+S2)
According to given condition, Time taken to cross train B in opposite direction = (4/7)*Time taken to cross train B in same direction
(9/5)*x / (S1 + S2) = (4/7)*[(9/5)*x / (S1 - S2)]
7(S1 - S2) = 4(S1 + S2)
3S1 = 11S2
S1/S2 = 11/3

Correct Option: 4 Best Solution (0)