15 men and 21 women, working together, can do a job in 56 days, while 12 men and 24 women, working together, can do the same job in 64 days. In how many days can the same job be done by 18 men and 24 women, working together?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 4)

Answer 1

Given:

15 men + 21 women can do a job = 56 days

12 men + 24 women can do a job = 64 days

Formula used:

Total work = efficiency × time

Calculation:

Let, the man efficiency = M

The woman efficiency = W

According to the question:

⇒ (15 M + 21 W) × 56 = (12 M + 24 W) × 64

⇒ (15 M + 21 W) × 7 = (12 M + 24 W) × 8

⇒ 105 M - 96 M = 192 W - 147 W

⇒ 9 M = 45 W

⇒ M/W = 5/1

Total work = (15 M + 21 W) × 56

⇒ {(15 × 5) + 21) × 56} = (96 × 56) units

Total efficiency = 18 M + 24 W

⇒ (18 × 5) + 24 × 1 = 114 units

Required time taken to complete work = Total work/total efficiency

⇒ (96 × 56)/114 = (16 × 56)/19 = 47 days

∴ The correct answer is 47 days.

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