A and B can do a work in 45 days and 40 days respectively.

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A and B can do a work in 45 days and 40 days respectively. They began the work together but A left after some time and B completed the remaining work in 23 days. After how many days of the start of the work did A leave ?

(A + B)’s 1 day’s work

=		1	+	1		=	17
		45		40			360

Work done by B in 23 days

=	1	× 23 =	23
	40		40

Remaining work = 1 -	23	=	17
	40		40

Now	17	work was done by (A + B) in 1 day
	360

∴	17	work was done by
	40

(A + B) in 1 ×	360	×	17	= 9 days.
	17		40

Hence, A left after 9 days.
Aliter : Using Rule 26,
Here, x = 45, y = 40, a = 23

⇒ Required time t =	(y - a)	× x
	(x + y)

t =	(40 - 23) × 45
	(45 + 40)

=	17 × 45	= 9 days
	85