Question

A boat goes $24$ km upstream and $28$ km downstream in $6$ hours. It goes $30$ km upstream and $21$ km downstream in $6$ hours and $30$ minutes. The speed of the boat on still water is

• A. $8$ km/hr
• B. $9$ km/hr
• C. $12$ km/hr
• D. $10$ km/hr

Answer 1

The correct option is D $10$ km/hr

Let speed of boat in still water = x km/hr
Let speed of stream = y km/hr
Upstream speed = (x - y) km/hr
Downstream speed = (x + y) km/hr.
Case I : $\frac{24}{x-y}+\frac{28}{x+y}=6$
Let $\frac{1}{x-y}=u$ & $\frac{1}{x+y}=v$
$24u+28v=6$ .....(1)
Case II : $\frac{30}{x-y}+\frac{21}{x+y}=\frac{13}{2}$
$30u+21v=\frac{13}{2}$ ......(2)
Multiplying eq.(1) by 3 & eq.(2) by 4, we get
$72u+84v=18$
120u + 84v = 26
$+48u=-8$
$u=\frac{1}{6}$ & $v=\frac{1}{14}$
$\frac{1}{6}=\frac{1}{x-y},\frac{1}{14}=\frac{1}{x+y}$
$x-y=6$ ......(3)
$x+y=14$ ......... (4)
On solving eq. (3) & (4)
x = $10$ & y = $4$
Hence, speed of boat in still water is $10$ kmph.