Question

A boat covers 12 km upstream and 18 km downstream in 3 hours, while it covers 36 km up- stream and 24 km downstream in 6$\frac{1}{2}$ hours. What is the speed of the current ?

• A. 1.5 kmph
• B. 1 kmph
• C. 2 kmph
• D. 2.5 kmph

Answer 1

Answer:

C. 2 kmph

Solution:

Let the speed of boat in still water be x kmph and that of current be y kmph, then

$\frac{12}{x+y}+\frac{12}{x-y}=3$ ----------(1)

$\frac{36}{x+y}+\frac{36}{x-y}=\frac{13}{2}$ ---------(2)

By $equation(1)\times3-equation(2)$,

$\frac{54}{x+y}-\frac{24}{x+y}=9-\frac{13}{2}$

$\frac{30}{x+y}=\frac{5}{2}$

$x+y=12$ -----------(3)

From Equation (1),

$\frac{12}{x-y}+\frac{18}{12}=3$

$\frac{12}{x-y}=3-\frac{18}{12}=3-\frac{3}{2}$

$x-y=\frac{12}{\frac{3}{2}}$

$x-y=4\times{2}=8$

Speed of current $=\frac{1}{2}(12-8)$

$=\frac{4}{2}=2 kmph$