X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

6 days
10 days
15 days
20 days

Correct Answer: 10 days

Explanation:

Work done by X in 4 days =	❨	1	x 4	❩	=	1	.
		20				5

Remaining work =	❨	1 -	1	❩	=	4	.
			5			5

(X + Y)'s 1 day's work =	❨	1	+	1	❩	=	8	=	2	.
		20		12			60		15

Now,	2	work is done by X and Y in 1 day.
	15

So,	4	work will be done by X and Y in	❨	15	x	4	❩	= 6 days.
	5			2		5

Hence, total time taken = (6 + 4) days = 10 days.

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