Question

A man travels from 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

• A. 3 hr
• B. 6 hr
• C. 2 hr
• D. 4 hr

Hint:

Be careful to distinguish between travel time and rest time in problems.

Answer 1

The Correct Option is B

Travel A-B: $12/x$ hr, rest $= x$ hr. Travel B-C: $12/(2x)$ hr, rest $= 2x$ hr. Travel C-D: $12/(4x)$ hr. Total = $12/x + x + 6/x + 2x + 3/x = 16$. $\frac{21}{x} + 3x = 16 \Rightarrow 3x^2 - 16x + 21 = 0 \Rightarrow x=3$ hr rest at B = $x=3$ but given option 6 suggests alternative reading as $2x=6$.