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Question
A man invested an amount at 10% per annum simple interest and another amount at 10% per annum simple interest. He received an annual interest of Rs. 1350. But, if he had interchanged the amounts invested, he would have received Rs. 45 less. What amounts did he invest at different rates?
Solution
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 = 13/50`
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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