A man lent a part of his money at $\displaystyle 10$% p.a. and the rest at $\displaystyle 15$% p.a. His income at the end of the year is ₹ $\displaystyle 1,900$ . If he had interchanged the rate of interest on the two sums, he would have earned ₹ $\displaystyle 200$ more. Find the amount lent in both cases.

Let amount lent for $\displaystyle 10$% p. a. \(\displaystyle =₹ x\) and amount lent for $\displaystyle 15$% p. a. \(\displaystyle =₹ y\) ATQ, \(\displaystyle \frac{10 x}{100}+\frac{15 y}{100}=1900\) or \(\displaystyle 2 x+3 y=38000\) and \(\displaystyle \frac{15 x}{100}+\frac{10 y}{100}=2100\) or \(\displaystyle 3 x+2 y=42000\) On solving these equations, we get \(\displaystyle x=10000\) and \(\displaystyle y=6000\) ∴ Amount lent for $\displaystyle 10$% p. a. = ₹ $\displaystyle 10000$ & money lent for $\displaystyle 15$% p. a. = ₹ $\displaystyle 6000$