Question

The sum of the salaries of A and B is ₹81,000. A spends 80% of his salary and B spends 70% of his salary. If their savings are in the ratio 4:3, then what is the salary of B?

• A. ₹ 25,400
• B. ₹ 27,000
• C. ₹ 26,500
• D. ₹ 54,000

Hint:

When dealing with ratios, always express the variables in terms of one another to simplify the problem. Use the sum equation to solve for the unknowns.

Answer 1

The Correct Option is B

Let the salary of A be \( A \) and the salary of B be \( B \). Given: \[ A + B = 81,000 \] Also, A spends 80% of his salary, so his savings are 20% of his salary, i.e., \( 0.20A \). B spends 70% of his salary, so his savings are 30% of his salary, i.e., \( 0.30B \). The ratio of their savings is given as 4:3: \[ \frac{0.20A}{0.30B} = \frac{4}{3} \] Simplifying: \[ \frac{2A}{3B} = \frac{4}{3} \quad \Rightarrow \quad 2A = 4B \quad \Rightarrow \quad A = 2B \] Substitute \( A = 2B \) into the equation \( A + B = 81,000 \): \[ 2B + B = 81,000 \quad \Rightarrow \quad 3B = 81,000 \quad \Rightarrow \quad B = 27,000 \] Thus, the salary of B is ₹ 27,000.