Prakash and Vinesh can complete a certain piece of work in 15 and 9 days, respectively, They started to work together, and after 5 days, Vinesh left. In how many days will Prakash complete the remaining work?

Correct option is B

Given:

Prakash can complete the work in 15 days

Vinesh can complete the work in 9 days

They worked together for 5 days, then Vinesh left

Formula Used:

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

Solution:

Prakash’s efficiency = $$\frac{1}{15}$$​​

Vinesh’s efficiency = $$\frac{1}{9}$$​​

Combined work in 3 days =  $$5\left( \frac{1}{15} + \frac{1}{9}\right)$$​​

​$$= 5 \left( \frac{8}{45} \right) = \frac{8}{9}$$​​

Remaining work = $$1 - \frac{8}{9} = \frac{1}{9}$$​​

Time for Prakash to finish $$\frac{1}{9}$$​ at rate $$\frac{1}{15}:$$​​

Time = $$\frac{1}{9} \div \frac{1}{15} = \frac{1}{9} \times 15 = \frac {15}9 days$$​​

Alternate Solution:

Let total work be 45 units (LCM of 15, 9).
=> Efficiency of Prakash =$$\frac{45}{15}$$​= 3 units/day

=> Efficiency of Vinesh = $$\frac{45}{9}$$​ = 5 units/day
=> Combined efficiency of Prakash and Vinesh = 3 + 5 = 8 units/day
=> Work done by Prakash and Vinesh in 5 days = 8 units/day × 5 days = 40 units
=> Remaining work = Total work - Work done = 45 - 40 = 5 units
=> Time taken by Prakash to complete the remaining work = Remaining work / Efficiency of Prakash
=> Time taken by Prakash = $$\frac 53 days$$ 
As option doesn't match multiply by 3 and divide by 3,  we get Time taken by Prakash = $$\frac {15}9 days$$