Boats and Streams Quiz Set 006

If the distance travelled is D and the speed of the current is R km/h, we have $D/{12/5 - R}$ = 3 × $D/{12/5 + R}$. Cancelling D, and solving for R, we get R = ${6/5}$ km/h. So downstream speed would be ${6/5}$ + $12/5$ = $3{3/5}$ km/h.

The downstream speed = $300/30$ = 10 km/h, and the upstream speed = $300/50$ = 6 km/h. By the shortcut method, the speed of the boat in still water is average of the downstream and upstream speeds of the boat. So the required speed = ${10 + 6}/2$ = 8 km/h.

The boats are same, so they have the same speed in still water. Let the upstream speed be u and v be the downstream speed, and let the initial distance between them be L. When they meet they have travelled for the same time. So $(L/6)/u = ({5L}/6)/v$. The ratio $v/u$ = 5.

Let the speed of the steamer in still water be u and the speed of the river be v. The three speeds are u - v, u and u + v. They are in an A.P. with a common difference equal to v. Since v is also the speed of the river, the required answer is: ${4/9}$.

Let v km/h be the rate of flow of the stream. Upstream and downstream times are equal. So $2/{112 - v}$ = $14/{112 + v}$. Solving for v, or verifying by putting the given options one by one, we get v = 84 km/h.