Swapnil can build a sofa in 16 days. Working together with Revathi he can finish the work in 128/17 days. Find the number of days taken by Revathi to complete the work if she works alone.

​​Given:
Time taken by Swapnil = 16 days
Combined time = 128/17 days
Formula Used:
Work = Time × Rate
Solution:  

Let Swapnil rate of work done be s and Revathi work rate be r.
Swapnil can do in 16 days

So, total work , w = 16s 

Now,  

​$$\frac{(s+r) \times {128}}{17} = 16 \times s \\ \ \\ r = \frac{16s \times 17}{128} - s \\ r = (1.125) s$$ 

So, putting s = $$\frac{w}{16}$$ 

​$$r = 1.125 \times \frac{w}{16} \implies w = \frac{r \times 16}{1.125} = (14.22)r$$ 

As we know, $$work(w) = rate(r)\times time(t)$$ 

 comparing, $$w = 14.22 \times r$$  

Thus, Time for Revathi to complete work alone = approx. 14.22 days = $$\frac{128}{9}\, days$$​​

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