Question

The salaries of A and B together amount to Rs. 26000/-. If they spend 75% and 60% of their respective salaries and their savings are equal, then their respective salaries should be

• A. Rs. 15,000, Rs. 10,000
• B. Rs. 18,000, Rs. 8,000
• C. Rs. 20,000, Rs. 6,000
• D. Rs. 16,000, Rs. 10,000

Hint:

Use algebraic ratios and total sum to find individual amounts.

Answer 1

The Correct Option is D

Let the salaries of A and B be \(x\) and \(y\) respectively.
Given:
\[ x + y = 26000 \] Savings of A = \(x - 0.75x = 0.25x\)
Savings of B = \(y - 0.60y = 0.40y\)
Their savings are equal:
\[ 0.25x = 0.40y \implies \frac{x}{y} = \frac{0.40}{0.25} = \frac{4}{2.5} = \frac{8}{5} \] So, \(x : y = 8 : 5\)
Step 1: Express \(x\) and \(y\) in terms of a common variable \(k\):
\[ x = 8k, y = 5k \] Step 2: Use total salary:
\[ 8k + 5k = 26000 \implies 13k = 26000 \implies k = 2000 \] Step 3: Calculate salaries:
\[ x = 8 \times 2000 = 16000 \] \[ y = 5 \times 2000 = 10000 \] Thus, the salaries are Rs. 16,000 and Rs. 10,000 respectively.