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

Options

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

Answer

To find the monthly expenses of the person, we can follow these steps:

### Step 1: Understand the given percentage of income spent
The person spends \(66 \frac{2}{3}\%\) of his income. This can be converted into a fraction:
\[ 66 \frac{2}{3}\% = \frac{200}{3}\% \]
To convert this percentage into a decimal, we divide by 100:
\[ \frac{200}{3} \div 100 = \frac{200}{300} = \frac{2}{3} \]

### Step 2: Determine the fraction of income saved
If the person spends \(\frac{2}{3}\) of his income, then the fraction of income saved is:
\[ 1 - \frac{2}{3} = \frac{1}{3} \]

### Step 3: Relate savings to income
We know that the savings per month is Rs. 1200. Since the savings represent \(\frac{1}{3}\) of his income, we can set up the equation:
\[ \frac{1}{3} \text{ (Income)} = 1200 \]

### Step 4: Calculate the total income
To find the total income, we multiply both sides of the equation by 3:
\[ \text{Income} = 1200 \times 3 = 3600 \]

### Step 5: Calculate monthly expenses
Now that we have the income, we can calculate the monthly expenses. Since the person spends \(\frac{2}{3}\) of his income, we calculate:
\[ \text{Expenses} = \frac{2}{3} \times 3600 \]
Calculating this gives:
\[ \text{Expenses} = \frac{2 \times 3600}{3} = \frac{7200}{3} = 2400 \]

### Conclusion
The monthly expenses of the person are Rs. 2400.

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