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 Rs. 4,000 and Rs. 900 from Rs. 5,000 of income, find $x\%$.

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

Answer 1

The correct option is B 15 %

According to the question
$\Rightarrow 2000\left(\frac{x}{100}\right)+(4000-2000)\left(\frac{y}{100}\right)=700$
$\Rightarrow 2000\left(\frac{x}{100}\right)+2000\left(\frac{y}{100}\right)=\mathrm{700........}eq1$
$\Rightarrow 2000\left(\frac{x}{100}\right)+(5000-2000)\left(\frac{y}{100}\right)=900$
$\Rightarrow 2000\left(\frac{x}{100}\right)+3000\left(\frac{y}{100}\right)=\mathrm{900......}eq2$
multiply eq1 by 3 and eq2 by 2 and substract
$\Rightarrow 2000\times \frac{x}{100}=300$
$\Rightarrow x=\frac{300\times 100}{200}=15$
Hence x%=15%