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 Rs 130. But if he had interchanged the amounts invested, he would have received Rs 4 more as interest. How much did he invest at 12% simple interest? (a) Rs 400 (b) Rs 500 (c) Rs 700 (d) Rs 800

Options

A. ₹500 at the rate of 10%.₹800 at the rate of 12%
B. ₹700 at the rate of 10%.₹600 at the rate of 12%
C. ₹800 at the rate of 10%.₹400 at the rate of 12%
D. ₹700 at the rate of 10%.₹500 at the rate of 12%

Answer

D

Explanation

Let the person inverst ₹ x and y at two different rates 12 % and 14 % respectively.
` ( x xx 12 xx 1)/100 + ( y xx 10 xx 1)/100 = 130 therefore ( SI = ( P xx R xx T)/100)`
` Rightarrow 12 x + 10y = 13000`
After inter changing invested amount .
`( y xx 12 xx 1)/100 + (x xx 10 xx 1)/100 = 134`
` Rightarrow 12y + 10x = 13400`
On solving equations ( i) and (ii) ,we get
x = ₹ 500 and y = ₹ 700