Question

a person invested some amount at the rate of 12% simple interest and some other amount at the rate of 10% simple interest. he received yearly interest of Rs.130 but if he had interchanged the amount invested, he would have received Rs.4 more as interest. how much amount did he invest at different rates?

Answer 1

Let the amount invested Rs x at the rate of 12% and Rs. y at the rate of 10%

according to the question 

simple intrest on Rs x at 12%  + simple intrest on Rs. y at 10% = 130 

we know simple intrest = (principle ×  rate × time )/100 and apply the formula

(x × 12 ×  1)/100 + ( y ×  10 ×  1)/100 = 130

12x + 10y = 13000  ......................( equation 1)

If he interchanged the amount invested , he would have received 4 more on intrest 

then

simple intrest on Rs x at 10% + simple intrest on Rs. y at 12 % = 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 multiply by 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 Rs and 10 % is 700

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

and the value is x = 500 Rs 

 y = 700 Rs.
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