Question

The time taken to travel 30km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11km then total time taken increases by 11 hours. Find the speed of the stream and speed of the boat.

• A. 4,7
• B. 7,8
• C. 3,2
• D. 6,3

Answer 1

The correct option is A

4,7

Lets assume that the speed of boat in still water is $x$ km/hr and speed of stream is $y$ km/hr.

Speed of boat upstream = $(x-y)$ km/hr.

Speed of boat downstream will be $(x+y)$ km/hr

Time = ( $\frac{distance}{speed}$)

First scenario -

$\frac{30}{x-y}$ + $\frac{44}{x+y}$ = 14 ......(i)

Second scenario

$\frac{60}{x-y}$ + $\frac{55}{x+y}$ = 25......(ii)

Let $\frac{1}{x-y}$ = u and $\frac{1}{x+y}$ = v

substituting u and v in (i) and (ii)

30u + 44v = 14.....(iii)

60u + 55v = 25......(iv)

Equation (iii) x 2

60u + 88v = 28

60u + 55v = 25

Subtracting the above two equations we get v = $\frac{1}{11}$

Substituting v in any of above two equations we get u = $\frac{1}{3}$

Since $\frac{1}{x-y}$ = u and $\frac{1}{x+y}$ = v

Substituting the values of u and v

$\frac{1}{x-y}$ = $\frac{1}{3}$ and $\frac{1}{x+y}$ = $\frac{1}{11}$

$\Rightarrow$ x - y = 3 and x + y = 11

Solving the above two equations we get x = 7, y = 4

So speed of boat in still water is 7 km/hr and speed of stream is 4 km/hr