Namita completes $$33\frac{1}{3}$$​% of a piece of work alone in 16 days and the remaining work is completed by Bobby alone. The entire work is completed in a total of 28 days. Working together, Namita and Bobby can complete $$\frac{11}{16}$$ part of the original work in:

Correct option is A

Given:

Namita completes $$33\frac{1}{3}\%$$​ of the work in = 16days

Time taken to complete the work = 28 days

Formula Used:

Let total work to fill the tank be 1.

Then work done by a pipe in 1 day $$=\frac{1}{Total\ time\ to\ taken\ to \ complete}$$​​

Solution:

Namita does $$33\frac{1}{3}\%$$​of the work in 16 days

​$$33\frac{1}{3}\% = \frac{100}{3}\% = \frac{100}{3}\times \frac{1}{100} = \frac{1}{3}$$​​

Time taken by Namita to complete $$\frac{1}{3}$$​rd of the work in 16 days

Hence time taken to complete the whole work = $$16 \times 3$$​ = 48 days

Bobby does the remaining work in = 28 - 16 = 12days

Remaining work $$= 1 - \frac{1}{3} =\frac{2}{3}$$​​

Bobby does the whole in = $$12 \times \frac{3}{2}$$ = 18days

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

Bobby’s one day’s work = $$\frac{1}{18}$$​​

Namita and Bobby’s one day work together =$$\frac{1}{48}+\frac{1}{18} =\frac{3+8}{144} =\frac{11}{144}$$​​

Work to be done = $$\frac{11}{16}$$​​

Time taken to complete the work =$$\frac{\frac{11}{16}}{\frac{11}{144}} = \frac{11}{16} \times \frac{144}{11}$$ = 9 days