A man, a boy and a woman can finish a work in 10 days, 15 days and 30 days, respectively. In how many days can the work be finished by a man, a woman and a boy when all of them work together?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 1)

Answer 1

Given:

Time taken by Man to finish a work = 10 days

Time taken by Boy to finish a work = 15 days

Time taken by a woman to finish a work = 30 days

Concept:

Since man, woman and boy finish the same work at different times, calculate their efficiencies using the formula M₁D₁ = M₂D₂ and proceed.

Formula used:

M₁D₁ = M₂D₂

Efficiency × No of days of work = Total Work

Calculation:

∵ 1 Man × 10 days = 1 Woman × 30 days = 1 Boy × 15 days

⇒ 2 Man = 6 Woman = 3 Boy

∴ The ratio of efficiency of a man, woman and boy = 3 ∶ 1 ∶ 2

Let the efficiency of man, woman and boy = 3a, a and 2a

Work done = 1 × 3a × 10 days

⇒ 30a

Together they will complete the work in:

⇒ 30a / (3a + a + 2a)

⇒ 5 days

The work is finished by a man, a woman and a boy when all of them work together in 5 days.