If 10 men or 20 women or 40 children can do a piece of work

Home » Aptitude » Time and Work » Question

If 10 men or 20 women or 40 children can do a piece of work in 7 months, then 5 men, 5 women and 5 children together can do half of the work in :

1. 6 months
2. 4 months
3. 5 months
4. 8 months

Correct Option: D

10 men ≡ 20 women
1 man = 2 women = 5 children
1 woman = 2 children
∴ 5 men + 5 women + 5 children = 20 + 10 + 5 = 35 children
∴ M₁D₁ = M₂D₂
⇒ 40 × 7 = 35 × D₂

⇒ D₂ =	40 × 7	= 8 months
	2

∴ 5 men, 5 women and 5 children can do half of the work in 8 months Required time = 4 months.
Aliter :
Using Rule 13, Here, A = 10, B= 20, C = 40, a = 7
A₁ = 5, B₁ = 5, C₁ = 5

Time taken to do same work =	a
	A₁	+	B₁	+	C₁
	A		B		C

=	7
	5	+	5	+	5
	10		20		30

=	7
	1	+	1	+	1
	2		4		8

=	7
	4 + 2 + 1
	8

= 8 months Half of the work they do in 4 months.