Question

A boat goes 16 km upstream and 24 km downstream in 6 hours. It can go 12 km upstream and 36 km downstream in the same time. Find the speed of the boat in still water and speed of the stream. *
1 point
a) 10 km/hr and 4km/ hr
b) 8 km/hr and 4km/ hr
c) 4 km/hr and 8 km/hr
d) 12 km/hr and 10 km/hr​

Answer 1

EXPLANATION

Let the speed of boat in still water = x km/hr

speed of the stream = y km/hr

Downstream speed of boat = (x + y) km/hr

upstream speed of boat = (x - y) km/hr

T = D/S

24/x + y + 16/x - y = 6 ......(1)

36/x + y + 12/x - y = 6 ......(2)

put 1/x + y = a and 1/x - y = b

Equation will be written as

24a + 16b = 6 ....(3)

6a + 2b = 1 ....(4)

solving equation (3) and (4) we get,

12a = 1

a = 1/12

and

b = 1/4

putting the value in 1/x + y and 1/x - y

1/x + y = 1/12 and 1/x - y = 1/4

x + y = 12....(5) and x - y = 4.....(6)

on solving this equation we get

2x = 16

x = 8

put x = 8 in equation (5) we get,

8 + y = 12

y = 4

speed of boat in still water = 8 km/hr

speed of stream = 4 km/hr

Hence,

option [B] is correct