If 6 men and 8 boys can do a piece of work in 10 days and

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If 6 men and 8 boys can do a piece of work in 10 days and 26 men and 48 boys can do the same in 2 days, then the time taken by 15 men and 20 boys to do the same type of work will be :

1. 5 days
2. 4 days
3. 6 days
4. 7 days

Correct Option: B

According to question,
(6M + 8B) × 10 = (26M + 48B) × 2
∴ 60M + 80B = 52M + 96B
or, 1M = 2B
∴ 15M + 20B = (30 + 20)B
= 50 boys and 6M + 8B
= (12 + 8) boys = 20 boys
∵ 20 boys can finish the work in 10 days
∴ 50 boys can finish the work in

	20 × 10	days = 4 days
	50

Aliter : Using Rule 11,
A₁ = 6, B₁ = 8, D₁ = 10
A₂ = 26, B₂ = 48, D₂ = 2
A₃ = 15, B₃ = 20
Required time

=	D₁D₂(A₁B₂ - B₁A₂	days
	D₁(A₁B₃ - A₃B₁) - D₂(A₂B₃ - A₃B₂)

=	10 × 2(6 × 48 - 8 × 26)	days
	10(6 × 20 - 15 × 8) - 2(26 × 20 - 15 × 48)

=	20(288 - 208)
	10(120 - 120) - 2(520 - 720)

=	20 × 80	= 4 days
	400