Question : Kanti and Jiya together can finish a work in 3 days. If Jiya alone can finish the work in 6 days, then in how many days can Kanti alone finish the work?
Option 1: 4 days
Option 2: 6 days
Option 3: 10 days
Option 4: 8 days
Correct Answer: 6 days
Solution :
Time taken by Jiya alone to finish the work = 6 days
⇒ Part of the work done by Jiya in a day = $\frac{1}{6}$
Let the time taken by Kanti alone to finish the work be $x$.
⇒ Part of the work done by Kanti in a day = $\frac{1}{x}$
Time taken by Kanti and Jiya together to finish a work = 3 days
⇒ Part of the work done by Kanti and Jiya in a day = $\frac{1}{3}$
So, $\frac{1}{6} + \frac{1}{x} = \frac{1}{3}$
⇒ $\frac{1}{x} = \frac{1}{3} - \frac{1}{6} = \frac{2-1}{6} = \frac{1}{6}$
$\therefore x = 6$
Hence, the correct answer is 6 days.
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