Question

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?

Answer 1

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let the amount invested rupees X at the rate of 12% and rupees Y at the rate of 10 % .

according to the question

simple interest on rupees x 12% + simple interest on Rupees by 10% = 130.

we know simple interest = ( principal ×rate ×time) / 100 and apply the formula.

( x×12×1)/100+(y×10×1)/100=130

12×10y=13000.......(equation 1 ).

if the interchanged amount invested he would have received 4 more on interest.

Then

simple interest on rupees X at 10% + simple interest on Rupees by 12% equal one 130 + 4

( x ×10×1)/100+(y×12×1)/100=134

10x +12y =13400.......(equation 2 )

solving both equation we will multiply by 12 in (equation 1 ) and X 10 in(equation 2 )

144x +120y=156000

100x +120y =134000

---( subtracting the equation).

44x = 22000
x =500

put the value of x =500 in equation 1

12×500+10y=13000

6000+10y=13000

10y=13000-6000

10y=7000

y=7000/10

y=700

the amount invested at 12 % is 500 rupees and 10 % 700

we use simple interest formula SI =(P×R×T)/100

and the value is x = 500 RS.

y=700

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