Varun can dig a garden bed in 10 days and Lakshmi in 15 days. They start together, but Varun stops 5 days before the digging is finished and Lakshmi completes it. How many days does the digging take in all?

Explanation

1. 01

   Let the total be $T$ days. Lakshmi works all $T$ days; Varun works $T - 5$.

2. 02

   $\frac{T-5}{10} + \frac{T}{15} = 1$. Multiply by 30: $3(T - 5) + 2T = 30$.

3. 03

   $5T = 45$, so $T = 9$ days.