Prakash and Vinesh can complete a certain piece of work in 10 and 8 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 B

Given:

Prakash can complete the work in 10 days

Vinesh can complete the work in 8 days

They worked together for 3 days, then Vinesh left

Formula Used:

Efficiency = $$\frac{1}{\text{Time to complete whole work}}$$​​

Solution:

Prakash’s efficiency = $$\frac{1}{10}$$​​

Vinesh’s efficiency = $$\frac{1}{8}$$​​

Combined work in 3 days =  $$3\left( \frac{1}{10} + \frac{1}{8}\right)$$​​

​$$= 3 \left( \frac{9}{40} \right) = \frac{27}{40}$$​​

Remaining work = $$1 - \frac{27}{40} = \frac{13}{40}$$​​

Time for Prakash to finish $$\frac{13}{40}$$​ at rate $$\frac{1}{10}:$$​​

Time = $$\frac{13}{40} \div \frac{1}{10} = \frac{13}{40} \times 10$$​​

​$$= \frac{130}{40}\text{ days}$$​​

Thus, Prakash will complete the remaining work in $$\frac{130}{40}$$​ days

Alternate Solution:

Total Work = Efficiency $$\times$$ Time​

Total work = 40 units (LCM of 10 and 8)

Prakash’s efficiency =$$\frac{40}{10}=$$​ 4 units/day

Vinesh’s efficiency =$$\frac{40}{8}=$$​ 5 units/day

Both worked together for 3 days

Work done in 3 days = (4 + 5) × 3 = 9 × 3 = 27 units

Remaining work = 40 - 27 = 13 units

Time for Prakash to complete = $$\frac{13}{4}$$​ = $$\frac{130}{40}$$​ days