Question

if the time taken by the boat to cover 60 km upstream and hundred km downstream is 20 hours find the time taken by the boat to cover 15 km upstream and 25 km downstream?
1)4 hours
2) 5 hours
3) 6 hours
4) 8 hours​

Answer 1

Answer:

Let the speed of the boat be 'b' and the speed of the stream be 's'.

According to the question,

{20/(b - s)} + {60/(b + s)} = 5 ----(i)

{30/(b - s)} + {80/(b + s)} = 7 ----(ii)

Let us put 1/(b - s) = P and 1/(b + s) = Q in equation (i) and (ii),

So,

20P + 60Q = 5 ----(iii)

30P + 80Q = 7 ----(iv)

Multiplying equation (iii) by 3 and equation (iv) by 2, we get

60P + 180Q = 15 ----(v)

60P + 160Q = 14 ----(vi)

Solving these we get,

(180 - 160)Q = 15 - 14

⇒ 20Q = 1

⇒ Q = 1/20

So, P = {5 - 60 × (1/20)}/20 ----{From equation (iii)}

⇒ P = {5 - (60/20)}/20

⇒ P = (5 - 3)/20

⇒ P = 2/20

⇒ P = 1/10

So, b - s = 10 & b + s = 20

So, b = 15 km/hr and s = 5 km/hr.

∴ The speed of the boat in still water is 15 km/hr.

Answer 2

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