Incomes of A and B are Rs 3500 and Rs 4200 respectively. The ratio of the savings of A and B is 4:3 and the ratio of their expenditures is 3:4. find the savings of A.

Options

A. Rs 800
B. Rs 600
C. Rs 900
D. Rs 1000

Answer

To find the savings of A, we can follow these steps:

### Step 1: Identify the given information
- Income of A = Rs. 3500
- Income of B = Rs. 4200
- Ratio of savings of A and B = 4:3
- Ratio of expenditures of A and B = 3:4

### Step 2: Express savings in terms of a variable
Let the savings of A be \(4k\) and the savings of B be \(3k\).

### Step 3: Calculate expenditures using the income and savings
- Expenditure of A = Income of A - Savings of A = \(3500 - 4k\)
- Expenditure of B = Income of B - Savings of B = \(4200 - 3k\)

### Step 4: Set up the ratio of expenditures
According to the problem, the ratio of expenditures of A and B is given as 3:4. Therefore, we can write:
\[ \frac{3500 - 4k}{4200 - 3k} = \frac{3}{4} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ 4(3500 - 4k) = 3(4200 - 3k) \]

### Step 6: Expand both sides
Expanding both sides results in:
\[ 14000 - 16k = 12600 - 9k \]

### Step 7: Rearrange the equation to isolate k
Rearranging gives:
\[ 14000 - 12600 = 16k - 9k \]
\[ 1400 = 7k \]

### Step 8: Solve for k
Dividing both sides by 7 gives:
\[ k = \frac{1400}{7} = 200 \]

### Step 9: Calculate the savings of A
Now that we have the value of \(k\), we can find the savings of A:
\[ \text{Savings of A} = 4k = 4 \times 200 = 800 \]

### Conclusion
The savings of A is Rs. 800.

---