Question

p and q can do a piece of work in 12 days and 15 days respectively. p started the work alone and then after 3 days q joined him till the work was completed how long did the work last​

Answer 1

The work lasts for 8 days.

Step-by-step explanation:

p takes 12 days to complete a work and q takes 15 days to complete the same work.

So, in one day p can complete $\frac{1}{12}$ of the work and q can complete $\frac{1}{15}$ of the work.

Now, p works for 3 days to complete $\frac{1}{12} \times 3 = \frac{1}{4}$ of the work.

So, the remaining $(1 - \frac{1}{4}) = \frac{3}{4}$ of the work they will work together.

Now, p and q together can do in one day $(\frac{1}{12} + \frac{1}{15}) = \frac{9}{60} = \frac{3}{20}$ of the work.

Therefore, p and q together will complete $\frac{3}{4}$ of the work in $(\frac{20}{3} \times \frac{3}{4}) = 5$ days.

Hence, the work lasts for (5 + 3) = 8 days. (Answer)