Question

A man earns $x%$ on the first Rs. 2{,}000 and $y%$ on the rest of his income. If he earns Rs. 700 from income of Rs. 4{,}000 and Rs. 900 from Rs. 5{,}000, find $x%$.

• A. 20%
• B. 15%
• C. 25%
• D. None of these

Hint:

In two-condition problems, set up separate equations for each condition and solve simultaneously.

Answer 1

The Correct Option is A

From the first case (income Rs. 4{,}000): First Rs. 2{,}000 earns at $x%$: $\frac{x}{100} \times 2000$ Next Rs. 2{,}000 earns at $y%$: $\frac{y}{100} \times 2000$ Total = 700 $\Rightarrow 20x + 20y = 700 \quad (1)$ From the second case (income Rs. 5{,}000): First Rs. 2{,}000 earns at $x%$: $\frac{x}{100} \times 2000$ Next Rs. 3{,}000 earns at $y%$: $\frac{y}{100} \times 3000$ Total = 900 $\Rightarrow 20x + 30y = 900 \quad (2)$ Subtract (1) from (2): $(20x + 30y) - (20x + 20y) = 900 - 700$ $10y = 200 \Rightarrow y = 20$ From (1): $20x + 20(20) = 700 \Rightarrow 20x + 400 = 700 \Rightarrow 20x = 300 \Rightarrow x = 15$ → correction here means answer is 15%, so option (b).