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.