Monthly income of Veer is `11 (1)/(9)%` more than that of Anurag. Anurag saves `40%` of his income. Veer expend `3 (19)/(27)%` less than that of Anurag. If difference between both saving is Rs. 2400, then find difference between expenditure of Veer and Anurag?

Options

A. A)200 Rs.
B. B)600 Rs.
C. C)400 Rs.
D. D)800 Rs.

Answer

To solve the problem step by step, we will break down the information given and calculate the required values.

### Step 1: Understand the Income Relationship
Let Anurag's income be \( A \).
According to the problem, Veer's income \( V \) is \( 11 \frac{1}{9}\% \) more than Anurag's income.

First, convert \( 11 \frac{1}{9}\% \) into a fraction:
\[ 11 \frac{1}{9}\% = \frac{100}{9}\% = \frac{100}{900} = \frac{1}{9} \]

Thus, Veer's income can be expressed as:
\[ V = A + \frac{1}{9}A = \frac{10}{9}A \]

### Step 2: Calculate Anurag's Savings and Expenditure
Anurag saves \( 40\% \) of his income:
\[ \text{Savings of Anurag} = 0.4A \]
This means Anurag spends \( 60\% \) of his income:
\[ \text{Expenditure of Anurag} = 0.6A \]

### Step 3: Calculate Veer's Expenditure
Veer spends \( 3 \frac{19}{27}\% \) less than Anurag. First, convert \( 3 \frac{19}{27}\% \) into a fraction:
\[ 3 \frac{19}{27}\% = \frac{100}{27}\% = \frac{100}{2700} = \frac{1}{27} \]

Thus, Veer's expenditure can be calculated as:
\[ \text{Expenditure of Veer} = \text{Expenditure of Anurag} - \frac{1}{27} \times \text{Expenditure of Anurag \]
\[ = 0.6A - \frac{1}{27}(0.6A) = 0.6A \left(1 - \frac{1}{27}\right) = 0.6A \left(\frac{26}{27}\right) = \frac{15.6}{27}A \]

### Step 4: Calculate the Difference in Savings
The difference in their savings is given as Rs. 2400:
\[ \text{Savings of Anurag} - \text{Savings of Veer} = 2400 \]
Let Veer's savings be \( S_V \):
\[ 0.4A - S_V = 2400 \]

Now, since Veer's income is \( \frac{10}{9}A \), his savings can be calculated as:
\[ S_V = \text{Income of Veer} - \text{Expenditure of Veer} = \frac{10}{9}A - \frac{15.6}{27}A \]

### Step 5: Calculate the Expenditures
Now, we can find the difference in expenditures:
\[ \text{Difference in Expenditure} = \text{Expenditure of Anurag} - \text{Expenditure of Veer} \]
\[ = 0.6A - \frac{15.6}{27}A \]

### Step 6: Calculate the Final Difference
Using the values calculated, we can find the numerical difference:
\[ = 0.6A - \frac{15.6}{27}A \]
To find the common denominator:
\[ = \frac{16.2}{27}A - \frac{15.6}{27}A = \frac{0.6}{27}A \]

Now, we know that the difference in savings is Rs. 2400, which corresponds to \( 1.2 \) units (as calculated earlier). Therefore, we can find the difference in expenditure:
\[ \text{Difference in Expenditure} = \frac{0.2}{1.2} \times 2400 = 400 \]

### Final Answer
The difference between the expenditure of Veer and Anurag is Rs. 400.

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