Salil and Aarav can do a piece of work in 45 and 40 days respectively. They began the work together but Salil...........

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Salil and Aarav can do a piece of work in 45 and 40 days respectively. They began the work together but Salil leaves after some days and Aarav finished the remaining work in 23 days.
After how many days did Salil leave?

posted Feb 4, 2016

Salil's speed = (1 work/45 days)
Aarav's speed = (1 work/40 days)
Speed*Time= Work
((1/45)+(1/40))*x + (1/40)*23 = 1
X=9
Therefore after 9 days salil leaves.

One day work of Salil and Aarav are 1/45 and 1/40 respectively.
One day work of both together=1/45 + 1/40
=(8+9)/360
=17/360
Let Salil and Aarav work together for x days
Work completed by both in x days=17 X/360
Remaining work=1-17X/360
=(360-17X)/360
This remaining work was completed by Aarav in 23 days.
and one day work of Aarav is 1/40
Work done by Aarav in 23 days=23/40=(360-17X)/360
9*23=360-17X
17X=360-207
17X=153
X=153/17
=9 Days

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