Arithmetic -5 (SNAP-2008)

A cyclist drove one kilometer with the wind in his back, in three minutes and drove the same way back against the wind in four minutes. If we assume that the cyclist always puts constant force on the pedals, how much time would it take him to drive one kilometer without wind?

(A)  7/3    (B)  24/7    (C)  17/7    (D) 43/12

Solution follows here:

Solution:

Let the speed of cyclist be ‘c’ and speed of wind be ‘w’.

When the wind is at his back, the resultant speed becomes c+w

Speed = distance/time => c+w = 1/3         ---(1)

When the wind is against him, the resultant speed becomes c-w

Speed = distance/time => c-w = 1/4          ---(2)

Adding (1) and (2), 2c = 1/3 + 1/4 = 7/12 => c = 7/24

Without wind, the speed is his sole speed ie.., ‘c’.

Time to drive 1 kilometer = distance/speed

= 1/c = 1/(7/24) = 24/7 minutes  

Answer (B)