X can do a piece of work in 24 days. When he had worked for 4 days. Y joined him. If complete work was finished in 16 days. Y alone can finish that work in.
A. 27 Days
B. 42 Days
C. 36 Days
D. 18 Days
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X can do a piece of work 24 days
In one day x can do 1/24 work
In 4 days x can do 4/24 work=1/6 w
Remaining work=1-1/6=5/6
the remaining work done by x+y in 16 days
5/6 work would be finished in => 16*6/5 =96/5 days .
According to the question the total work was finished in 16 days
4+(96-x)/5=16
X=36 days
Let Y can finish alone in y days.
Here X works for 16 days and Y works for (16-4)=12 days.
16*1/24 +12*1/y=1
y=36
Y alone can finish in 36 days.
X can complete the work in 24 days.
So, work done by X in 1 day = 1/24th work
Therefore, work done by him in 4 days = 4*1/24 = 1/6th work
Remaining work to be finished by both X and Y = 1 -1/6 = 5/6
They finish it in (16-4) i.e 12 days. Therefore, work done by both in 1 day = (5/6)/12 = 5/ 72.
Now, work done in 1 day by X alone = 1/24
Therefore, work done by Y alone in 1 day = 5/72 - 1/24 = 2/72 = 1/36
Hence, Y alone can finish the work in 1/(1/36) i.e 36 days.