A person who spends 66 `2/3` % of his income is able to save 1,200 per month. His monthly expenses(in Rs.) is:

Options

A. A) 1200
B. B) 2400
C. C) 3000
D. D) 3200

Answer

To solve the problem, we need to find the monthly expenses of a person who spends 66 2/3% of his income and saves Rs. 1200 per month.

### Step-by-Step Solution:

1. **Convert the percentage to a fraction:**
- The percentage given is 66 2/3%.
- To convert this to a fraction, we first convert the mixed number:
\[ 66 \frac{2}{3} = \frac{66 \times 3 + 2}{3} = \frac{198 + 2}{3} = \frac{200}{3} \]
- Thus, 66 2/3% can be written as:
\[ \frac{200}{3} \% \]

2. **Understand the relationship between income, expenses, and savings:**
- If the person spends 66 2/3% of his income, then he saves the remaining percentage:
\[ 100\% - 66 \frac{2}{3}\% = 33 \frac{1}{3}\% \]
- This can also be converted to a fraction:
\[ 33 \frac{1}{3} = \frac{33 \times 3 + 1}{3} = \frac{100}{3} \% \]

3. **Set up the equation:**
- Let the total income of the person be \( I \).
- The savings can be expressed as:
\[ \text{Savings} = \frac{100}{3} \% \text{ of } I = \frac{100}{3} \times \frac{I}{100} = \frac{I}{3} \]
- According to the problem, the savings amount to Rs. 1200:
\[ \frac{I}{3} = 1200 \]

4. **Calculate the income:**
- To find the income \( I \), we can multiply both sides of the equation by 3:
\[ I = 1200 \times 3 = 3600 \]

5. **Calculate the monthly expenses:**
- The expenses are 66 2/3% of the income:
\[ \text{Expenses} = \frac{200}{3} \% \text{ of } 3600 = \frac{200}{3} \times \frac{3600}{100} \]
- Simplifying this:
\[ \text{Expenses} = \frac{200 \times 3600}{3 \times 100} = \frac{720000}{300} = 2400 \]

### Final Answer:
The monthly expenses of the person are Rs. 2400.

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