Two carpenters, Manoj and Rehana, can make a set of classroom benches together in 12 days. They work together for 5 days, then Rehana leaves and Manoj finishes the rest alone in 21 days. How many days would Rehana take to make the whole set alone?

Explanation

1. 01

   In 5 days together: $\frac{5}{12}$ done, leaving $\frac{7}{12}$.

2. 02

   Manoj does $\frac{7}{12}$ in 21 days, so his rate is $\frac{7}{12} \div 21 = \frac{1}{36}$ per day.

3. 03

   Rehana's rate = $\frac{1}{12} - \frac{1}{36} = \frac{2}{36} = \frac{1}{18}$.

4. 04

   Rehana alone takes 18 days.