Question

acing is he fol 3. A boatman rows his boat 35 km upstream and 55 km downstream in 12 h. He can row 30 km upstream and 44 km downstream in 10 h, then the speed of the boat in still water is (a) 8 km/h (b) 3 km/h (c) 5 km/h (d) 11 km/h ​

Answer 1

Answer:

a) 8 km/hr

Explanation:

Given that a boatman rows his boat 55 km downstream and 35 km upstrêam in 12 hours. He can row 44 km downstream and 30 km upstream in 10 hours.

Let's say that the speed of boat in still water = x km/h and speed of current = y km/h

Therefore,

Upstream speed = Speed of boat in still water - speed of current = x - y

Down-strēam speed = Speed of boat in stïll water + speed of currēnt = x + y

Now,

Time = distance/speed

A boat goes 35 km upstrēam and 55 km down.stream in 12 hours.

12 = 35/(x - y) + 55/(x + y) ------- (1)

It co.vērs 30 km upstrēam and 44 km down-stream in 10 hours.

10 = 30/(x - y) + 44/(x + y) -------- (2)

Let's say 1/(x - y) = a and 1/(x + y) = b

12 = 35a + 55b ------- (3)

10 = 30a + 44b

2(5) = 2(15a + 22b)

5 = 15a + 22b ………. (4)

Sub-traçt (3) and (4) also multiply eq (3) by 2 and eq (4) by 5

On solving we get

5a = 1

a = 1/5 or 1/(x - y) = 5

x - y = 5

Substitute a = 1/5 in eq (4) and on solving we get,

b = 1/11 or 1/(x + y) = 11

x + y = 11

On adding x + y = 11 and x - y = 5 we get,

x = 8 and y = 3

Hence, Speed of the boat in still water = 8 Km/hr & Speed of the stream = 3 km/hr.