2 men and 3 women can do a piece of work in 10 days while

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2 men and 3 women can do a piece of work in 10 days while 3 men and 2 women can do the same work in 8 days. Then, 2 men and 1 woman can do the same work in

1. 12 days
2. 12 1 days
  2
3. 13 days
4. 12 1 days
  2

Correct Option: B

2 × 10 men + 3 × 10 women
= 3 × 8 men + 2 × 8 women
⇒ 20 men + 30 women = 24 men + 16 women
⇒ 4 men = 14 women or 2 men = 7 women
∴ 2 men + 3 women = 10 women
∴ 2 men + 1 woman = 8 women
∴ M₁D₁ = M₂D₂
⇒ 10 × 10 = 8 × D₂

⇒ D₂ =	25	= 12	1	days
	2		2

Aliter :
22 (Using Rule 11),
Here, A₁ = 2, B₁ = 3, D₁ = 10
A₂ = 3, B₂ = 2, D₂ = 8
A₃ = 2, B₃ = 1

Required time =	D₁D₂(A₁B₂ - A₂B₁)	days
	D₁(A₁B₃ - A₃B₁) - D₂(A₂B₃ - A₃B₂)

=	10 × 8(2 × 2 - 3 × 3)	days
	10(2 × 1 - 2 × 3) - 8(3 × 1 - 2 × 2)

=	10(2 × 4 - 9)	days
	10(2 - 6) - 8(3 - 4)

=	- 400	=	25
	- 32		2

= 12	1	days
	2