Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Numbers, Quantification and Numerical Applications

Question:

A motor boat can travel at 12 km/hr in still water. It travelled 63 km downstream in river and then returned back taking altogether 24 hours. The speed of the water current in the river is:

Options:

12 km/hr

9 km/hr

6 km/hr

10 km/hr

Correct Answer:

9 km/hr

Explanation:

$\text{Speed in still water}=12.$

$\text{Let speed of current}=v.$

$\text{Downstream speed}=12+v.$

$\text{Upstream speed}=12-v.$

$\frac{63}{12+v}+\frac{63}{12-v}=24.$

$\frac{63(12-v)+63(12+v)}{144-v^2}=24.$

$\frac{63(24)}{144-v^2}=24.$

$1512=24(144-v^2).$

$1512=3456-24v^2.$

$24v^2=1944.$

$v^2=81.$

$v=9.$

$\text{Speed of water current}=9\text{ km/hr}.$