If $\frac{1}{5}$ of $\frac{3}{4}$ of a $\frac{1}{3}$ of the number is 24,then 20% of that number is :

Question

Accepted Answer

To solve the problem, we need to find the original number based on the given condition and then calculate 20% of that number.

1. **Understanding the Problem:**
   - We are given that $\frac{1}{5}$ of $\frac{3}{4}$ of $\frac{1}{3}$ of a number is 24.
   - Let's denote the number as $x$.

2. **Setting Up the Equation:**
   - According to the problem, $\frac{1}{5} \times \frac{3}{4} \times \frac{1}{3} \times x = 24$.

3. **Solving for $x$:**
   - Simplify the expression: $\frac{1}{5} \times \frac{3}{4} \times \frac{1}{3} = \frac{1}{20}$.
   - Therefore, $\frac{1}{20} \times x = 24$.
   - Multiply both sides by 20 to solve for $x$: $x = 24 \times 20 = 480$.

4. **Calculating 20% of the Number:**
   - Now that we know $x = 480$, we need to find 20% of this number.
   - 20% of 480 is calculated as: $\frac{20}{100} \times 480 = 96$.

5. **Conclusion:**
   - Therefore, 20% of the number is 96, which corresponds to Option 3.

6. **Explanation of Other Options:**
   - **Option 1 (66):** This is incorrect because 20% of 480 is not 66.
   - **Option 2 (72):** This is incorrect because 20% of 480 is not 72.
   - **Option 4 (48):** This is incorrect because 20% of 480 is not 48.

By following the logical steps and calculations, we have confirmed that Option 3 (96) is indeed the correct answer.