The monthly salaries of A and B together amount to Rs. 40000. A spends 85% of his salary and B, 95% of his salary. If now their savings are the same, then the salary (In Rs.) of A is

Options

A. A) Rs.10,000
B. B) Rs.12,000
C. C) Rs.16,000
D. D) Rs.18,000

Answer

To solve the problem step by step, let's denote the salaries of A and B as \( S_A \) and \( S_B \) respectively.

### Step 1: Set up the equations based on the given information.
We know that the total salary of A and B together is Rs. 40,000. Therefore, we can write:
\[ S_A + S_B = 40000 \]

### Step 2: Express the savings of A and B.
A spends 85% of his salary, which means he saves 15% of his salary. Thus, A's savings can be expressed as:
\[ \text{Savings of A} = 0.15 S_A \]
Similarly, B spends 95% of his salary, so he saves 5% of his salary:
\[ \text{Savings of B} = 0.05 S_B \]

### Step 3: Set the savings of A equal to the savings of B.
According to the problem, their savings are the same:
\[ 0.15 S_A = 0.05 S_B \]

### Step 4: Rearrange the equation to express \( S_B \) in terms of \( S_A \).
We can rearrange the equation:
\[ S_B = \frac{0.15}{0.05} S_A = 3 S_A \]

### Step 5: Substitute \( S_B \) back into the total salary equation.
Now substitute \( S_B \) in the total salary equation:
\[ S_A + 3 S_A = 40000 \]
This simplifies to:
\[ 4 S_A = 40000 \]

### Step 6: Solve for \( S_A \).
Now, divide both sides by 4:
\[ S_A = \frac{40000}{4} = 10000 \]

### Conclusion:
The salary of A is Rs. 10,000.

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