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:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 20.
A can complete the work in 20 days,
so Rate of A =1/20 work per day
B can complete the work in 10 days,
so Rate of B = 1/10 work per day
Combined rate = 1/5 work per day
The combined rate of A, B, and C is the sum of their individual rates:
⇒ Rate of A + Rate of B + Rate of C = 1/5
⇒ 1/20 + 1/10 + Rate of C = 1/5
⇒ Rate of C = 1/5 - 1/20 - 1/10 = (4 - 1 - 2)/20 = 1/20
then C alone can complete the work =
Time for C = 1/Rate of C = 20 days