8 men can complete a work in 45 days. 8 women can complete the same work in 18 days. In how many days will 5 men and 8 women, together, complete the same work?

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SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 1)
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  1. \(13 \frac{1}{5} \)
  2. \(12 \frac{4}{5}\)
  3. \(14 \frac{2}{5} \)
  4. \(15 \frac{3}{5}\)

Answer (Detailed Solution Below)

Option 3 : \(14 \frac{2}{5} \)
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Detailed Solution

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Given:

Total time taken by 8 men to complete the work = 45 days

Total time taken by 8 women to complete the work = 18 days

Formula used:

Total work = Total efficiency × Total time

Calculation:

Let, M = Man and W = Woman

So, 8M × 45 = 8W × 18

⇒ M/W = 2/5

∴ A man can do = 2 work/day

∴ A woman can do = 5 work/day

Total work = (8 × 2) × 45 = 720

The total work done by 5 men and 8 women for one day = (5 × 2) + (8 × 5)

= 50 

So, the total time is taken by them ⇒ 720/50 ⇒ 14(2/5)

The work will be completed in 14(2/5) days.

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