Question

A boat can cover 14 km upstream and 30 km downstream in 6 hours, while it covers 24 km upstream and 18 km downstream in 7.5 hours. What is the speed of the boat?

1. 10 km/h
2. 8 km/h
3. 12 km/h
4. 16 km/h

Answer 1

Correct Answer - Option 2 : 8 km/h

Given:

Upstream distance vovered = 14 km

Downstream covered = 30km

 Time (T1)= 6 hrs

Upstream distance = 24 km

Downstream distance = 18 km

Time (T2) = 7.5 hrs

Calculation:

Let, speed of the boat = x = km/h and speed of stream = y km/h

According to the question,

⇒ (14/(x ─ y)) + (30/(x + y)) = 6

⇒ (42/(x ─ y)) + (90/(x + y)) = 18        …(1)

According to the question,

⇒ (24/(x ─ y)) + (18/(x + y)) = 7.5

⇒ (120/(x ─ y)) + (90(x + y)) = 37.5    ……(2)

From (2) – (1) we get,

⇒ 78/(x ─ y) = 19.5

⇒ x – y = 4    ……(3)

From (1) we get,

⇒  (42/4) + (90/(x + y)) = 18

⇒ 10.5 + (90/(x + y)) = 18

⇒ 7.5 × (x + y) = 90

⇒ x + y = 12    ……(4)

From (4) – (3) we get,

⇒ 2x = 16

⇒ x = 8

∴ Speed of the boat = 8 km/hr