Prakash and Vinesh can complete a certain piece of work in 12 and 14 days, respectively, They started to work together, and after 3 days, Vinesh left. In how many days will Prakash complete the remaining work?

Correct option is A

Given:

Prakash can complete the work in 12 days.

Vinesh can complete the work in 14 days.

They work together for 3 days, after which Vinesh leaves.

Concept Used:

Prakash's rate: $$\frac{1}{12}$$​ (work per day).

Vinesh's rate: $$\frac{1}{14}​$$​ (work per day).

The combined work done in 3 days is the sum of the individual work rates for 3 days.

Solution:

Calculate the combined work rate of Prakash and Vinesh:

​$$\frac{1}{12} + \frac{1}{14} = \frac{7}{84} + \frac{6}{84} = \frac{13}{84}​$$​​

Work done by both in 3 days: Total work done

​$$\text{Total work done} = 3 \times \frac{13}{84} = \frac{39}{84} = \frac{13}{28} ​$$​​

The remaining work after 3 days: Remaining work= $$\frac{13}{28} = \frac{28}{28} - \frac{13}{28} = \frac{15}{28}$$ 

Time for Prakash to complete the remaining work 

​$$\frac{\frac{15}{28}}{\frac{1}{12}} = \frac{15}{28} \times 12 = \frac{180}{28} = \frac{45}{7}$$days

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