A certain number of men can do a piece of work in 40 days.

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A certain number of men can do a piece of work in 40 days. If there were 45 men more the work could have been finished in 25 days. Find the original number of men employed in the work.

Original number of men = x (let)
∴ M₁ D₁ = M₂ D₂
⇒ x × 40 = (x + 45) × 25
⇒ 8x = (x + 45) × 5
⇒ 8x = 5x + 225
⇒ 8x – 5x = 225
⇒ 3x = 225

⇒ x =	225	= 75 men
	3

Aliter : Using Rule 23,
Here, D = 40, a = 45, d = (40 – 25) = 15

∴ Required number=	a(D - d)
	d

=	45(40 - 15)
	15

=	45 × 25	= 15 × 5 = 75
	15