The incomes of A and B are in the ratio 5:3. The expenses of A, B and Care in the ratio 8:5:2. If C spends 2000 and B saves 700, then A saves

Options

A. रु 1500
B. रु 1000
C. रु 500
D. रु 250

Answer

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

### Step 1: Understand the Ratios
The incomes of A and B are in the ratio of 5:3. This means if A's income is 5 parts, then B's income is 3 parts.

### Step 2: Set Up Variables for Incomes
Let the incomes of A and B be represented as:
- Income of A = 5p
- Income of B = 3p

### Step 3: Understand the Expenses Ratios
The expenses of A, B, and C are in the ratio of 8:5:2. We can represent their expenses as:
- Expenses of A = 8x
- Expenses of B = 5x
- Expenses of C = 2x

### Step 4: Find the Value of x
We know that C spends 2000, which means:
\[ 2x = 2000 \]
From this, we can find x:
\[ x = \frac{2000}{2} = 1000 \]

### Step 5: Calculate the Expenses of A and B
Now we can calculate the expenses of A and B using the value of x:
- Expenses of A = \( 8x = 8 \times 1000 = 8000 \)
- Expenses of B = \( 5x = 5 \times 1000 = 5000 \)

### Step 6: Calculate B's Income
We know that B saves 700. Therefore, B's income can be calculated as:
\[ \text{Income of B} = \text{Expenses of B} + \text{Savings of B} \]
\[ \text{Income of B} = 5000 + 700 = 5700 \]

### Step 7: Find A's Income Using the Ratio
Since the incomes of A and B are in the ratio of 5:3, we can set up the equation:
\[ \frac{\text{Income of A}}{\text{Income of B}} = \frac{5}{3} \]
Let the income of A be \( 5k \) and the income of B be \( 3k \). We already know that B's income is 5700, so:
\[ 3k = 5700 \]
From this, we can find k:
\[ k = \frac{5700}{3} = 1900 \]
Now, we can find A's income:
\[ \text{Income of A} = 5k = 5 \times 1900 = 9500 \]

### Step 8: Calculate A's Savings
Now we can find A's savings:
\[ \text{Savings of A} = \text{Income of A} - \text{Expenses of A} \]
\[ \text{Savings of A} = 9500 - 8000 = 1500 \]

### Final Answer
A saves **1500**.

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