Question

Priya can complete a work in 16 days. Priya and Prachi require 9 days to finish the work if they work together. Find the number of days required if Prachi works alone.​

Answer 1

Given:

Priya can complete the work in 16 days.

Priya and Prachi work together and complete the work in 9 days.

To find:

We need to find in how many days Prachi can do alone the work.

Solution:

Priya can complete work in 16 days = $\frac{1}{16}$

Priya and Prachi work together and complete in 9 days = $\frac{1}{9}$

Now, we need to find the Prachi work alone.

So, we need to subtract the work together and Priya work.

=  $\frac{1}{9} - \frac{1}{16}$

Now, we need to take LCM and calculate the values.

The LCM of 16 and 9 is 144.

= $\frac{16 - 9}{144}$

= $\frac{7}{144}$

= $\frac{1}{2.5}$            

Prachi can work alone in 2.5 days.