Question : Anshu, Swati, and Rajni can finish a work in 4 days if they work together. However, Anshu alone will take 9 days to complete the work, and Swati alone will complete the work in 12 days. How many days will Rajni alone take to complete the work?
Option 1: 18
Option 2: 12
Option 3: 24
Option 4: 16
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Correct Answer: 18
Solution :
Time taken by Anshu to complete the work = 9 days
Work done by Anshu in a day = $\frac{1}{9}$
Time taken by Swati to complete the work = 12 days
Work done by Swati in a day = $\frac{1}{12}$
Time taken by them to complete the work together = 4 days
Work done by them in a day together = $\frac{1}{4}$
Let the time taken by Rajni to complete the work be $x$ days
Time taken by Rajni to complete the work = $\frac{1}{x}$
So, $\frac{1}{9} + \frac{1}{12} + \frac{1}{x} = \frac{1}{4}$
Or, $\frac{1}{x} = \frac{1}{4} - (\frac{1}{9} + \frac{1}{12} )$
Or, $\frac{1}{x} = \frac{1}{18}$
Or, $x = 18$ days
Hence, the correct answer is 18.
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