A man and a woman can finish a work together in half the time taken by a woman and a boy together. A boy can finish the work alone in 20 days and 2 women together can finish it in 30 days. In how many days will the work be finished by 4 men?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 18 Jul 2023 Shift 4)

Answer 1

Given:

Time taken by (man + woman) = (1/2) × Time taken by (woman + boy)

A boy alone can finish the work = 20 days

2 women can finish the work = 30 days.

Concept used:

If total work is constant then,

Time ∝ (1/efficiency)

Formula used:

Total work = efficiency × time

Calculation:

2 women can finish the work = 30 days.

1 woman can finish the work = 30 × 2 = 60 days

Now,

Time taken by (man + woman) = (1/2) × Time taken by (woman + boy)

Time taken by (man + woman) : Time taken by (woman + boy) = 1 : 2

Efficiency of (man + woman) : Efficiency of (woman + boy) = 2 : 1

(Woman + boy) = (3 + 1) = 4

⇒ 1 unit = 4 units/day

⇒ 2 units = 4 × 2 = 8 units/day

Efficiency of (man + woman) = 8

Efficiency of man = 8 - 1 = 7 units/day

Time taken to complete the work by 4 men = 60/(4 × 7)

⇒ 60/28 = 15/7 = 2.14 days

∴ The correct answer is 2.14 days.

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