1.

A boatman rows some distance upstream and some distance downstream. If the time taken by the man to row upstream is twice the time taken by him to row downstream. Find the ratio of distance travelled by the man upstream to that of downstream, if the speed of boat in still water is 7 km / hr and the speed of stream is 2 km / hr?1. 12 ∶ 132. 10 ∶ 93. 4 ∶ 54. 9 ∶ 75. 15 ∶ 8

Answer» Correct Answer - Option 2 : 10 ∶ 9

Given

The speed of boat in still water is 7 km / hr.

The speed of stream is 2 km / hr.

The time taken by the man to row upstream is twice the time taken by him to row downstream

Formula used

Let u and v be the speed of boat in still water and speed of stream respectively.

Speed upstream = (u - v)

Speed downstream = (u + v)

Calculations

Let the distance travelled upstream = x km

And the distance travelled downstream = y km

Speed upstream = (u - v) = 7 - 2 = 5 km / hr

Speed downstream = (u + v) = 7 + 2 = 9 km / hr

Time taken by the man to row upstream is = \(\frac{{\rm{x}}}{5}\)

Time taken by the man to row downstream is = \(\frac{{\rm{y}}}{9}\)

The time taken by the man to row upstream is twice the time taken by him to row downstream ∶

\(\Rightarrow \frac{x}{5} = \left( {\frac{y}{9}} \right) \times 2\)

⇒ x ∶ y = 10 ∶ 9

Hence the ratio of distance travelled by the man upstream to that of downstream is 10 ∶ 9.


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