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If 6 women and 12 girls can do a piece of work in 12 days and 12 women and 8 girls can do same piece of work in 9 days, in how many days do 10 women and 15 girls complete that piece of work?
1. 288/35 days
2. 10 days
3. 144/35 days
4. 15 days

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Correct Answer - Option 1 : 288/35 days

Given:

6 women and 12 girls can do a piece of work in 12 days and 12 women and 8 girls can do same piece of work in 9 days.

Concepts used:

M1 × D1/W1 = M2 × D2/W2 

Where, M = Number of men, D = Number of days, H = Number of hours, W = Work

Calculation:

6 women (w) and 12 girls (g) can do a piece of work in 12 days (D1) and 12 women (w) and 8 girls (g) can do same piece of work in 9 days (D2).

⇒ (6w + 12g) × 12/1 = (12w + 8g) × 9/1

⇒ 72w + 144g = 108w + 72g

⇒ 108w – 72w = 144g – 72g

⇒ 36w = 72g

⇒ 1w = 2g

Let 10 women and 15 girls complete a piece of work in D days.

⇒ (6w + 12g) × 12/1 = (10w + 15g) × D/1 

⇒ (6 × 2 g + 12g) × 12 = (10 × 2g + 15g) × D

⇒ 24g × 12 = 35g × D

⇒ 288g = 35g × D

⇒ D = 288g/35g

⇒ D = 288/35 days

∴ 10 women and 15 girls can do a piece of work in 288/35 days.

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