Question : Rimmi and Simmi can together finish a work in 40 days. They worked together for 30 days and then Simmi left. After another 30 days, Rimmi finished the remaining work alone. In how many days Rimmi alone can finish the work?
Option 1: 120 days
Option 2: 30 days
Option 3: 80 days
Option 4: 40 days
Correct Answer: 120 days
Solution :
Time taken by Rimmi and Simmi can together finish a work = 40 days
1 day's work of them = $\frac{1}{40}$
They work together for 30 days.
So, work done by them in 30 days = $\frac{1}{40}×30=\frac{3}{4}$
$\therefore$ Remaining work = $1-\frac{1}{30}=\frac{1}{4}$
Time taken by Rimmi to finish the remaining work = 30 days
$\therefore$ Time taken by Rimmi to finish the whole work = $\frac{30}{\frac{1}{4}}=30×4= 120$ days
Hence, the correct answer is 120 days.
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