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The speed of boat A is 2 km/h less than the speed of the boat B. The time taken by boat A to travel a distance of 20 km downstream is 30 min more than time taken by B to travel the same distance downstream. If the speed of the current is 1/3rd of the speed of the boat A, what is the speed of boat B?


A) 4

B) 6

C) 12

D) 10

E) 8

Correct Answer:
E) 8

Description for Correct answer:
Let the speed of boat B x + 2 km/hr

The speed of boat A is x kh/hr.

Speed of the current = \( \frac{1}{3} \times x = \frac{x}{3} km/hr \)

Accroding to question,

\( \frac{20}{x+\frac{x}{3}} \) - \( \frac{20}{(x+2)+\frac{x}{3}} \)

= \( \frac{30}{(60} \)

\( \frac{20 \times 3}{4x} - \frac{20 \times 3}{4x+6} = \frac{1}{2} \)

\( \frac{4x+6-4x}{4x \left(4x+6\right) } = \frac{1}{120}\)

\( \frac{6}{16x^{2}+24x} = \frac{1}{120} \)

\( 16x^{2}+24x-720=0 \)

\( 2x^{2}+3x-90=0 \)

\( 2x^{2}+15x-12x-90=0 \)

\( x \left(2x+15\right)-6 \left(2x+15\right)=0 \)

\( \left(x-6\right) \left(2x+15\right)=0 \)

x = 6

Hence, the speed of boat B = x + 2 = 6 + 2 = 8 km/hr

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