Case 1: when A wins by 1/10 of a minute time:

Distance covered by A = 480 m.
Distance covered by B = 480 - 48 = 432 m
Time taken by A = t1 sec
Time taken by B = t1 + (1/10 of a min= 1/10 *60=6) = (t1 + 6) sec

note: u have to find ans in m/s

Case 2: when B wins by 1/30 of a minute time
Distance covered by A = 480
Distance covered by B = (480 -144)= 336
Time taken by B = t2 sec
Time taken by A = t2 + (1/30 of a min= 1/30 *60=2) = t2+2 sec

Remember speed of A and B remain same in both cases, so equate above unknowns as:
Speed = Distance/ Time (in m/s)
Speed of A = 480/t1 = 480/(t2+2) [-> eqn 1]
Speed of B = 432/(t1 + 6) = 336/t2 [-> eqn 2]

-> from 1st eqn: t2+2 =t1,
replace t1 in eqn 2 with (t2+2)

432/(t2+2+6) = 336/t2
after solving this I got: t2=28 sec

Speed of B = 336/t2 = 336/28 = 12 m/s.

so A is the correct ans as per my knowledge and calculation.

arjunsekhar wrote:6. A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B's speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20


[spoiler]Ans: A[/spoiler]

1/10th of minute = 6 seconds
1/30th of minute = 2 seconds.

When B got 48m head start, B was 6 seconds behind.
When B got 144m head start, B was 2 seconds ahead.

Which means, B travelled, (144-48)m in 6+2 = 8 seconds
=96m in 8 seconds
speed = 96/8 = 12m/sec

pick A.

Hope this helps!!

Thanks a lot guys....really cleared it up .