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# A, B and C can do a piece of work in 20,30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

**Given:**

A, B and C can do a piece of work in 20,30 and 60 days respectively.

**To do:**

We have to find the time required to complete the work if A does the work every day and he is assisted by B and C on every third day.

**Solution:**

Number of days required to complete the work by A$=20$ days.

Work done by A in one day$=\frac{1}{20}$

Number of days required to complete the work by B$=30$ days.

Work done by B in one day$=\frac{1}{30}$

Number of days required to complete the work by C$=60$ days.

Work done by C in one day$=\frac{1}{60}$

Work done by A in three days $=3\times\frac{1}{20}=\frac{3}{20}$

Therefore,

Work done by A, B and C in three days if A is assisted by B and C every third day$=\frac{3}{20}+\frac{1}{30}+\frac{1}{60}=\frac{3\times3+1\times2+1\times1}{60}=\frac{12}{60}=\frac{1}{5}$

This implies,

The time required to complete the work if A is assisted by B and C every third day$=3\times\frac{1}{\frac{1}{5}}=3\times5=15$ days.