10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

A boat travels with a speed of \[\text{15 km}/\text{h}\] in still water. In a river flowing at \[\text{5 km}/\text{hr},\]the boat travels some distance downstream and them returns. The ratio of average speed to the speed in still water is:

A) \[8:3\]

B) \[3:8\]

C) \[8:9\]

D) \[9:8\]

Correct Answer: C

Solution :

[c] Let distance =d

Time taken upstream \[=\frac{d}{15-5}=\frac{d}{10}\]

Time taken downstream \[=\frac{d}{15+5}=\frac{d}{20}\]

Hence, average speed

\[=\frac{2d}{\frac{d}{10}+\frac{d}{20}}=\frac{2d\times 20}{3d}=\frac{40}{3}km/hr\]

Ratio \[=\frac{40}{3}:15=40:45=8:9\]