Question

A person invested some amount at the rate of 10% simple interest and some amount at the rate of 12% simple interest. He received an yearly interest of Rs 130. But if he had interchanged the amounts invested, he would have received Rs 4 more as interest. How much amounts did he invest at 12% and 10% respectively ? 

(a) Rs 600, Rs 550 

(b) Rs 800, Rs 450 

(c) Rs 700, Rs 500 

(d) Rs 500, Rs 700

Answer 1

(d) Rs 500, Rs 700

Suppose the person invested Rs a at 12% simple interest and Rs b at 10% simple interest. Then,

\(\frac{12a}{100}+\frac{10b}{100}\) = 130  \(\Rightarrow\) 6a + 5b = 6500 ..........(i)

If the amounts invested are interchanged, then the yearly interest = Rs 134

\(\therefore\) \(\frac{10a}{100}+\frac{12b}{100}\) = 134  \(\Rightarrow\) 5a + 6b = 6700 .........(ii)

Now we can solve the equations for a and b.