12 men and 16 boys can do a piece of work in 5 days, while 13 men and 24 boys can do it in 4 days. In how many days can 29 men and 22 boys complete the work?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 3)

Answer 1

Given:

(12 men + 16 boys) can do a piece of work = 5 days

(13 men + 24 boys) can do a piece of work = 4 days

Formula used:

Total work = efficiency × time

Calculation:

Let, the efficiency of man = M

The efficiency of boy = B

According to the question:

⇒ (12 M + 16 B) × 5 = (13 M + 24 B) × 4

⇒ 60 M - 52 M = 96 B - 80 B

⇒ 8 M = 16 B

⇒ M/B = 2/1

Total work = (12 M + 16 B) × 5

⇒ {(12 × 2) + (16 × 1)} × 5

⇒ (24 + 16) × 5 = 40 × 5 = 200 units

Required time to complete the work = 200/{(29 × 2) + (22 × 1)}

⇒ 200/(58 + 22) = 200/80

⇒ 5/2 = 2.5 days

∴ The correct answer is 2.5 days.

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