A flask contains a mixture of two compounds AB and XY. Both of these decompose on heating by first order reaction. If the half-life of AB is 30 min and that of XY is 10 min, how long will it take for the concentration of AB to be four times that of XY ? Assume that the initial concentration of both AB and XY to be same.

Explanation

To solve the problem, we need to analyze the decomposition of the two compounds, AB and XY, which are undergoing first-order reactions. We are given the half-lives of both compounds and need to find out how long it will take for the concentration of AB to be four times that of XY.

### Step-by-Step Solution:

1. **Understanding First-Order Reactions**:
The concentration of a reactant in a first-order reaction can be expressed as:
\[
[A] = [A_0] \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}
...