Question : Pawan can do a piece of work in 32 days. He worked for 8 days and left the work. Thereafter Sandeep finished the remaining work in 27 days. In how many days can Pawan and Sandeep together do the whole work?
Option 1: $16 \frac{16}{17}$ days
Option 2: $16 \frac{13}{17}$ days
Option 3: $16 \frac{15}{17}$ days
Option 4: $16 \frac{14}{17}$ days
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Correct Answer: $16 \frac{16}{17}$ days
Solution :
Let the total work be represented by $W$.
Pawan can complete the work in 32 days, so his daily work rate is $\frac{W}{32}$.
Pawan worked for 8 days, so the work done by Pawan in 8 days is $8\times\frac{W}{32}=\frac{W}{4}$.
The remaining work to be done is $W-\frac{W}{4} = \frac{3W}{4}$
Now, Sandeep will finish the remaining work in 27 days.
Sandeep's daily work rate is $\frac{\frac{3W}{4}}{27}=\frac{3W}{108}=\frac{W}{36}$
Now, let $x$ be the number of days Pawan and Sandeep together can do the whole work.
The work done by Pawan in $x$ days is $x\times\frac{W}{32}$
The work done by Sandeep in $x$ days is $x\times\frac{W}{36}$
The sum of their work must equal the total work:
⇒ $\frac{W}{32}x+\frac{W}{36}x=W$
⇒ $\frac{9W}{288}x + \frac{8W}{288}x = W$
⇒ $\frac{17W}{288}x = W$
⇒ $x = \frac{288}{17} = 16\frac{16}{17}$
Hence, the correct answer is $16\frac{16}{17}$ days.
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