Ravi can complete a certain job in 48 days. Kiran is 60% more efficient than Ravi. In how many days will they together complete- the same job?

Correct option is B

Given:

Time taken by Ravi to complete the job = 48days

Kiran is 60% more efficient than Ravi

Formula Used:

Let total work be 1.

Then work done 1 day =$$\frac{1}{Total\ time\ to\ work}$$​​

Work done = Efficiency of each worker $$\times$$​ Time

Solution:

Ravi’s one day work =$$\frac{1}{48}$$​​

Then Kiran’s is 60% more efficient then Kiran’s one day work = $$\frac{1}{48} + 60\% \ of \ \frac{1}{48} = \frac{1}{30}$$​​

Then work done by both Ravi and Kiran together in one day =$$\frac{1}{48} + \frac{1}{30} =\frac{10+16}{480} =\frac{13}{240}$$​​

Total time required by both Ravi and Kiran working together =$$\frac{1}{\frac{13}{240}} =\frac{240}{13} = 18\frac{6}{13}$$​days

Hence, option(b) is correct

Alternative Method:

Let the efficiency of Ravi be x

Then efficiency of Kiran will be = x + 60% of x = 1.6x

Total efficiency of both Ravi and Kiran working together = x + 1.6x = 2.6x

Total work = Total days required by Ravi $$\times$$​ Efficiency = 48x

Time required by both Ravi and Kiran working together =$$\frac{Total\ Work}{Efficiency} = \frac{48x}{2.6x} = \frac{480}{26} =18\frac{6}{13}$$​days