Hemant and Irfan can complete a certain piece of work in 9 and 14 days, respectively, They started to work together, and after 3 days, Irfan left. In how many days will Hemant complete the remaining work?

Correct option is A

Given:

Hemant can complete the work in 9 days.

Irfan can complete the work in 14 days.

Hemant and Irfan worked together for 3 days.

Formula Used:

Work Done = Rate of Work × Time

Solution:

Hemant's rate of work is $$\frac{1}{9}$$​ of the work per day.

Irfan's rate of work is $$\frac{1}{14}$$​ of the work per day.

​Work done by Hemant and Irfan together in 1 day:

​$$\frac{1}{9} + \frac{1}{14}$$​

So, together, their combined rate of work is:

​$$\frac{14}{126} + \frac{9}{126} = \frac{23}{126}$$​

Work done by Hemant and Irfan together in 3 days:

Work Done =$$\frac{23}{126} \times 3 = \frac{69}{126} = \frac{23}{42}$$​

So, in 3 days, they completed $$\frac{23}{42}$$​ of the work.

The remaining work is:

​$$1 - \frac{23}{42} = \frac{42}{42} - \frac{23}{42} = \frac{19}{42}$$​

Time taken by Hemant to complete the remaining work:
Hemant works at a rate of $$\frac{1}{9}$$​ per day, so the time required for him to complete the remaining $$\frac{19}{42}$$​ of the work is:

Time =$$\frac{\frac{19}{42}}{\frac{1}{9}} = \frac{19}{42} \times 9 = \frac{171}{42}$$​ days

Alternate Method:

LCM of 9 and 14 = 126

This means in one day, we can consider the total work as 126 parts.

Hemant completes $$\frac{126}{9} =$$​ 14 parts per day.

Irfan completes $$\frac{126}{14}$$​ = 9 parts per day.
Together, Hemant and Irfan complete:

14 + 9 = 23 parts per day

So, their combined rate of work is 23 parts per day.
In 3 days, they will complete:

23 × 3 = 69 parts

The total work is 126 parts, so after 3 days, the remaining work is:

126 − 69 = 57 parts
Now, Hemant has to complete the remaining 57 parts. Since Hemant works at a rate of 14 parts per day,

the time Hemant will take to complete the remaining work is:

​$$\frac{57}{14} = \frac{171}{42} \text{days}$$​