A person invested some amount at the rate of 12\% simple interest and a certain amount at the rate of 10\% simple interest. He received yearly interest of ₹ 130. But if he had interchanged the amounts invested, he would have received ₹ 4 more as interest. How much did he invest at 12\% simple interest?
(a)₹ 400
(b)₹ 500
(c)₹ 700
(d)₹ 800
Answer
Answer (as printed): B
Explanation
Let the amount invested at 12\% be ₹ $x$ and that invested at 10\% be ₹ $y$. Then, $12 \%$ of $x+10 \%$ of $y=130$ $$\Rightarrow \quad 12 x+10 y=13000 \Rightarrow 6 x+5 y=6500$$ And, 10\% of $x+12 \%$ of $y=134$ $$\Rightarrow \quad 10 x+12 y=13400 \Rightarrow 5 x+6 y=6700$$ Adding (i) and (ii), we get: $11(x+y)=13200$ $$\Rightarrow \quad x+y=1200$$ Subtracting (i) from (ii), we get: $-x+y=200$ Adding (iii) and (iv), we get: $2 y=1400$ or $y=700$. Hence, amount invested at $12 \%=(1200-700)=₹ 500$.
Explanation as extracted from the printed page; notation may be imperfect.