A, B and C can complete an work in 12, 15 and 25 days resctively. A and B started working together where area C worked with them in every third day. find the number of days required to complete the work.

In first 6 days, C will work just two days but A and B will work 6 days.

So total work done by them in 6 days will

= $$\begin{gathered} \left(6\times \frac{1}{12}\right)+\left(6\times \frac{1}{15}\right)+\left(2\times \frac{1}{25}\right) \\ = \frac{1}{2}+\frac{2}{5}+\frac{2}{25} \\ = \frac{25+20+4}{50} \\ =\frac{49}{50 } \end{gathered}$$

Remaining work =$1-\frac{49}{50}=\frac{1}{50}$ part of the work.

So. (A and B) 1 day's work= $\frac{1}{12}+\frac{1}{15}=\frac{4+5}{60}=\frac{9}{60}=\frac{3}{20}$

In 7^th day. C will not help them. Only A and B will do the $\frac{1}{50}$  part of the work because $\frac{3}{20}>\frac{1}{50}$ 

Now, $\frac{3}{20}$ part of the work is done by A and B in 1 day 

$\frac{1}{50}$ part of the work is done by A and B in = $\frac{20}{3}\times \frac{1}{50}=\frac{2}{15}$ day 

Total work will be completed in = $\left(6+\frac{2}{15}\right)=6\frac{2}{15}$ days 

ans. The number of days required to complete the work is $6\frac{2}{15}$ days