The sum of the salaries of A and B together is 43000. A spends 95% of his salary and B, 80% of his salary. If now their savings are the same, what is B's salary (in Rs.)?

Options

A. 8600
B. 34400
C. 10600
D. 48600

Answer

To solve the problem, let's break it down step by step.

### Step 1: Define the Variables
Let A's salary be \( x \) and B's salary be \( y \).

### Step 2: Set Up the First Equation
According to the problem, the sum of the salaries of A and B is 43,000. Therefore, we can write the first equation as:
\[ x + y = 43000 \quad \text{(1)} \]

### Step 3: Determine the Savings of A and B
A spends 95% of his salary, which means he saves 5% of his salary. Thus, A's savings can be expressed as:
\[ \text{Savings of A} = 0.05x \]

B spends 80% of his salary, which means he saves 20% of his salary. Thus, B's savings can be expressed as:
\[ \text{Savings of B} = 0.20y \]

### Step 4: Set Up the Second Equation
According to the problem, A's savings are equal to B's savings. Therefore, we can write the second equation as:
\[ 0.05x = 0.20y \quad \text{(2)} \]

### Step 5: Simplify the Second Equation
We can simplify equation (2) by multiplying both sides by 100 to eliminate the decimals:
\[ 5x = 20y \]
Now, divide both sides by 5:
\[ x = 4y \quad \text{(3)} \]

### Step 6: Substitute Equation (3) into Equation (1)
Now we will substitute equation (3) into equation (1):
\[ 4y + y = 43000 \]
This simplifies to:
\[ 5y = 43000 \]

### Step 7: Solve for B's Salary
Now, divide both sides by 5 to find \( y \):
\[ y = \frac{43000}{5} = 8600 \]

### Conclusion
Thus, B's salary is:
\[ \text{B's Salary} = 8600 \text{ Rs.} \]