Ratio of income of A to that of B is `5:9` .If expenditure of A is `3/8` th of his income and expenditure of B is `4/9` th of his income and sum of their saving is Rs 1950 then find the difference between their income ?

Options

A. A)Rs 900
B. B)Rs 1000
C. C)Rs 880
D. D)Rs 960

Answer

To solve the problem step by step, we will follow the details provided in the question and the video transcript.

### Step 1: Define the Income of A and B
Given the ratio of incomes of A and B is 5:9, we can represent their incomes as:
- Income of A = 5x
- Income of B = 9x

### Step 2: Calculate Expenditure of A and B
According to the problem:
- Expenditure of A = \( \frac{3}{8} \) of his income
- Expenditure of B = \( \frac{4}{9} \) of his income

Calculating the expenditures:
- Expenditure of A = \( \frac{3}{8} \times 5x = \frac{15x}{8} \)
- Expenditure of B = \( \frac{4}{9} \times 9x = 4x \)

### Step 3: Calculate Savings of A and B
Savings can be calculated as:
- Savings of A = Income of A - Expenditure of A
- Savings of B = Income of B - Expenditure of B

Calculating the savings:
- Savings of A = \( 5x - \frac{15x}{8} \)
- To simplify, convert \( 5x \) to a fraction with a denominator of 8:
- \( 5x = \frac{40x}{8} \)
- Therefore, Savings of A = \( \frac{40x}{8} - \frac{15x}{8} = \frac{25x}{8} \)

- Savings of B = \( 9x - 4x = 5x \)

### Step 4: Sum of Savings
According to the problem, the sum of their savings is Rs 1950:
\[ \text{Savings of A} + \text{Savings of B} = 1950 \]
\[ \frac{25x}{8} + 5x = 1950 \]
Convert \( 5x \) to a fraction with a denominator of 8:
\[ 5x = \frac{40x}{8} \]
Thus, we have:
\[ \frac{25x}{8} + \frac{40x}{8} = 1950 \]
\[ \frac{65x}{8} = 1950 \]

### Step 5: Solve for x
To find x, multiply both sides by 8:
\[ 65x = 1950 \times 8 \]
\[ 65x = 15600 \]
Now, divide by 65:
\[ x = \frac{15600}{65} = 240 \]

### Step 6: Calculate Incomes
Now that we have x, we can find the incomes:
- Income of A = \( 5x = 5 \times 240 = 1200 \)
- Income of B = \( 9x = 9 \times 240 = 2160 \)

### Step 7: Find the Difference in Incomes
The difference between their incomes is:
\[ \text{Difference} = \text{Income of B} - \text{Income of A} = 2160 - 1200 = 960 \]

### Final Answer
The difference between their incomes is Rs 960.

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