If 3/5 of 60% of a Number is 36, then the value of the number is :

Question

Accepted Answer

To solve the problem, we need to find the value of the number such that 3/5 of 60% of this number equals 36.

Let's break down the problem step by step:

1. **Understanding the Expression**: 
   - We are given that 3/5 of 60% of a number is 36.
   - Mathematically, this can be expressed as: 
     $$
     \frac{3}{5} \times 0.6 \times \text{Number} = 36
     $$

2. **Simplifying the Expression**:
   - First, calculate 60% as a decimal, which is 0.6.
   - Then, multiply 0.6 by 3/5:
     $$
     \frac{3}{5} \times 0.6 = \frac{3 \times 0.6}{5} = \frac{1.8}{5} = 0.36
     $$

3. **Setting Up the Equation**:
   - Now, we have:
     $$
     0.36 \times \text{Number} = 36
     $$

4. **Solving for the Number**:
   - To find the number, divide both sides of the equation by 0.36:
     $$
     \text{Number} = \frac{36}{0.36} = 100
     $$

5. **Conclusion**:
   - Therefore, the value of the number is 100, which corresponds to Option 2.

**Explanation for Other Options**:

- **Option 1 (60)**: 
  - If the number were 60, then 3/5 of 60% of 60 would be:
    $$
    \frac{3}{5} \times 0.6 \times 60 = \frac{3 \times 36}{5} = \frac{108}{5} = 21.6
    $$
  - This does not equal 36, so Option 1 is incorrect.

- **Option 3 (120)**:
  - If the number were 120, then 3/5 of 60% of 120 would be:
    $$
    \frac{3}{5} \times 0.6 \times 120 = \frac{3 \times 72}{5} = \frac{216}{5} = 43.2
    $$
  - This does not equal 36, so Option 3 is incorrect.

- **Option 4 (150)**:
  - If the number were 150, then 3/5 of 60% of 150 would be:
    $$
    \frac{3}{5} \times 0.6 \times 150 = \frac{3 \times 90}{5} = \frac{270}{5} = 54
    $$
  - This does not equal 36, so Option 4 is incorrect.

Thus, the correct answer is indeed Option 2, which is 100.