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Question

A man travels A to B at a speed x km/hr. He then rests at B for x hours. He then travels from B to C at a speed 2x km/hr and rests for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hr. If distances A-B, B-C and C-D are all equal to 12 km, the time for which he rested at B could be : (1996)

A
3 hr
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B
6hr
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C
2hr
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D
4hr
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Solution

The correct option is A 3 hr

Using answer options :
Option (a) total time taken from A to D.
12x+x+122x+2x+124x=16
21x+3x=16
3x216x+21=0
x=3 , 37

Alternatively:
Going by the answer options:
Let us assume the answer to be 2 hrs.

FROM-TOSpeedTime taken to cover 12 kmsRest timeCumulative timeAB2628BC4347CD81.501.5Total time taken16.5

Let us assume the answer to be 3 hrs.
FROM-TOSpeedTime taken to cover 12 kmsRest timeCumulative timeAB3437BC6268CD12101Total time taken16


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