12 men and 12 women can complete a piece of work in 9 days. 6 men and 15 women can complete the same work in 12 days. How long (in days) would it take 9 women to complete half the work?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 07 Dec 2022 Shift 4)

Answer 1

Given:

12 men and 12 women can complete a piece of work in 9 days.

6 men and 15 women can complete the same work in 12 days.

Calculation:

Let efficiency of man be M unit and efficiency of woman be W unit.

According to the question

Total work = (12M + 12W) × 9 ---(1)

Total work = (6M + 15W) × 12 ---(2)

⇒ (12M + 12W) × 9 = (6M + 15W) × 12

⇒ 108M + 108W = 72M + 180W

⇒ 36M = 72W

⇒ M : W = 2 : 1

Total work = (6M + 15W) × 12

⇒ (6 × 2 + 15 × 1) × 12

⇒ (12 + 15) × 12

⇒ 324

9 women to complete the half of the work = 324/2 × 1/9

⇒ 18 days

∴ 18 days taken by 9 women to complete half of the work.