Question

The speed of stream is $\frac{4{5}$ of the speed of a boat in still water. If the boat covers 198 km in 11 hours downstream, then find the difference of time taken by boat to cover 60 km in upstream and 36 km downstream.}

• A. 24 h
• B. 26 h
• C. 28 h
• D. 20 h

Hint:

Use: Downstream speed = boat + stream speed; Upstream speed = boat - stream speed. Time = Distance / Speed. Find 's' from given data, then calculate times.

Answer 1

The Correct Option is C

Let the speed of the boat in still water be $5s$ km/h, so the speed of the stream is $\frac{4}{5} \times 5s = 4s$ km/h. - Downstream speed = boat speed + stream speed = $5s + 4s = 9s$ km/h. - Given downstream distance = 198 km, time = 11 hours, so: \[ 9s = \frac{198}{11} = 18 \implies s = 2 \] - Therefore, Boat speed = $5s = 10$ km/h, Stream speed = $4s = 8$ km/h. - Upstream speed = boat speed - stream speed = $10 - 8 = 2$ km/h. - Time to cover 60 km upstream = $\frac{60}{2} = 30$ hours. - Time to cover 36 km downstream = $\frac{36}{10+8} = \frac{36}{18} = 2$ hours. - Difference in time = $30 - 2 = 28$ hours.