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
• B. 6hr
• C. 2hr
• D. 4hr

Answer 1

The correct option is A 3 hr

Using answer options :
Option (a) total time taken from A to D.
$\frac{12}{x}+x+\frac{12}{2x}+2x+\frac{12}{4x}=16$
$\to \frac{21}{x}+3x=16$
$\to 3x^2-16x+21=0$
$\to x=3,\frac{3}{7}$

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

$\begin{array}{ccccc}\text{FROM-TO}& \text{Speed}& \text{Time taken to cover 12 kms}& \text{Rest time}& \text{Cumulative time}\\ A-B& 2& 6& 2& 8\\ B-C& 4& 3& 4& 7\\ C-D& 8& 1.5& 0& 1.5\\ Totaltimetaken& & & & 16.5\end{array}$

Let us assume the answer to be 3 hrs.
$\begin{array}{ccccc}\text{FROM-TO}& \text{Speed}& \text{Time taken to cover 12 kms}& \text{Rest time}& \text{Cumulative time}\\ A-B& 3& 4& 3& 7\\ B-C& 6& 2& 6& 8\\ C-D& 12& 1& 0& 1\\ Totaltimetaken& & & & 16\end{array}$