Correct Answer - Option 1 : 15 km/hr
Given:
Time taken by boat to cover 20 km upstream and 60 km downstream = 5 hrs.
Time taken by boat to cover 60 km upstream and 80 km downstream = 7 hrs.
Concept Used:
If 'b' is the speed of a boat and 's' is the speed of a stream then,
Upstream speed of boat = b - s
& Downstream speed of boat = b + s
Calculation:
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.