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A boat covers 20 km upstream and 60 km downstream in 5 hours. Boat covers 30 km upstream and 80 km downstream in 7 hours. What is the speed of boat in still water?
1. 15 km/hr
2. 20 km/hr
3. 14 km/hr
4. 12 km/hr

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Best answer
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. 

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