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A can complete a piece of work in 20 days and B can complete the same work in 10 days. With the help of C, working together they completed the work in
Question

A can complete a piece of work in 20 days and B can complete the same work in 10 days. With the help of C, working together they completed the work in 5 days. The number of days in which C alone can complete the work is:

A.

25

B.

10

C.

15

D.

20

Correct option is D

Given:
A can do a piece of work = 20 days
B can do a piece of work = 10 days
(A+B+C) can do the work in 5 days
Concept Used :
Let Pipe A can fill the tank in x hrs.
Pipe A can fill a tank in 1 hrs = 1x\frac{1}{x}​​
Solution :
A's 1 day's work = 120 \frac{1}{20}​​
B's 1 day's work = 110\frac{1}{10}​​
(A+B+C)'s 1 day's work = 15\frac{1}{5}​​
Let, C can complete the work in = x days
C's 1 day's work =  1x\frac{1}{x}​​
According to question,
110+120+1x=15 =>1x=(421)20 =>1x=120 =>x=20\frac{1}{10}+\frac{1}{20} + \frac{1}{x} =\frac{1}{5} \\\ \\=>\frac{1}{x} = \frac{(4-2-1)}{20}\\\ \\=>\frac{1}{x} = \frac{1}{20}\\\ \\=> x = 20​​
∴ C alone can complete the work in 20 days.

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