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# A man invested an amount at 10% per annum and another amount at 8% per annum simple interest .Thus,he received Rs.1350 as annual interest .Had he interchanged the amounts invested ,he would have received Rs.45 less as interest .What amounts did he invest at different rates?

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This question is taken from linear equations in two variables in which we have to calculate the invested amount if the total interest received is 1350 from two different interest rates 8% and 10%.

Kindly solve the above problem

RS Aggarwal, class 10, chapter 3E, question no 28

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### 1 Answer

1. Let the amounts invested at 10% and 8% be Rs.x and Rs.y respectively.

Then as per the question

x × 10 × 1/ 100 = y × 8 × 1/ 100 = 1350

10x + 8y = 135000 …………..(i)

After the amounts interchanged but the rate being the same, we have

x × 8 × 1/ 100 = y × 10 × 1/ 100 = 1350 – 45

8x + 10y = 130500 …………….(ii)  Adding (i) and (ii) and dividing by 9, we get

2x + 2y = 29500 ……………(iii)  Subtracting (ii) from (i), we get

2x – 2y = 4500

Now, adding (iii) and (iv), we have  4x = 34000

x = 34000/4 = 8500

Putting x = 8500 in (iii), we get

2 × 8500 + 2y = 29500

2y = 29500 – 17000 = 12500

y = 12500/2 = 6250

Hence, the amounts invested are Rs. 8,500 at 10% and Rs. 6,250 at 8%.

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