Question

A boat goes 24 km upstream and 28 km dowstream in 6 hours. If it goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes, find the speed of the stream.

• A. 10 km/hr
• B. 5 km/hr
• C. 4 km/hr
• D. 6 km/hr

Answer 1

The Correct Option is C

Assume the speed of boat be \(x\ \frac{km}{hr}\)

the speed of boat be stream \(y\ \frac{km}{hr}\)

The speed in Downstream = \((x + y) \frac{km}{hr}\)

The speed in Upstream \((x - y) \frac{km}{hr}\)

Given in the question,

\(\frac{24}{x - y} + \frac{28}{x + y} = 6\)  – (i)

\(\frac{30}{x - y} + \frac{21}{x + y} = 6.5\)  – (ii)

By multiplying equation (i) with -3 and equation (ii) with 4 we get,

\(\frac{48}{x - y} = 26 - 18\)

\(x - y = \frac{48}{8} = 6\)  – (iii)

\(x + y = 14\)   – (iv)

Subtracting equation (iii) from equation (iv) we get,

\(y = \frac{8}{2} = 4\)

The correct option is (C): 4 km/hr