Question : Pinki and Rinki together can do a piece of work in 20 days. Rinki and Minki together can do it in 12 days while Pinki and Minki together can do it in 15 days. For how long can Rinki alone do it?
Option 1: 20 days
Option 2: 25 days
Option 3: 30 days
Option 4: 10 days
Correct Answer: 30 days
Solution :
Let the rates at which Pinki, Rinki, and Minki can complete the work as P, R, and M as work per day, respectively.
From the problem,
Pinki and Rinki together can do the work in 20 days.
⇒ P + R = $\frac{1}{20}$
Rinki and Minki together can do the work in 12 days.
⇒ R + M = $\frac{1}{12}$
Pinki and Minki together can do the work in 15 days.
⇒ P + M = $\frac{1}{15}$
Solve these equations by adding the first and second equations and then subtracting the third equation,
⇒ 2R = $\frac{1}{20} + \frac{1}{12} - \frac{1}{15} = \frac{4}{60}$
⇒ R = $\frac{1}{30}$
$\therefore$ Rinki alone can do the work in 30 days.
Hence, the correct answer is 30 days.
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