3 men and 4 boys can complete a piece of work in 12 days.

Home » Aptitude » Time and Work » Question

3 men and 4 boys can complete a piece of work in 12 days. 4 men and 3 boys can do the same work in 10 days. Then 2 men and 3 boys can finish the work in

1. 17 1 days
  2
2. 5 5 days
  11
3. 8 days
4. 22 days

Correct Option: A

12 (3 men + 4 boys)
≡ 10 (4 men + 3 boys)
⇒ 36 men + 48 boys = 40 men + 30 boys
⇒ 4 men = 18 boys
⇒ 2 men = 9 boys
∴ 4 men + 3 boys
= 21 boys, who do the work in 10 days and 2 men + 3 boys = 12 boys
∴ M₁D₁ = M₂D₂
⇒ 21 × 10 = 12 × D₂

⇒ D₂ =	21 × 10	=	35	= 17	1	days
	12		2		2

Aliter :
Using Rule 11, Here, A₁ = 3, B₁ = 4, D₁ = 12
A₂ = 4, B₂ = 3, D₂ = 10
A₃ = 2, B₃ = 3

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

=	12 × 10(3 × 3 - 4 × 4)	days
	12(3 × 3 - 2 × 4) - 10(4 × 3 - 2 × 3)

=	120 × - 7	days
	12(9 - 8) - 10 × 6

=	- 840	= 17	1	days
	- 48		2