A man invested an amount at 12 % per annum simple interest and another amount at 10 % per annum simpel interest. He received an annual interest fo ₹ 2600. But, if he had intercharged the amounts invested, he would havr received ₹ 140 less. What amounts did he invest at the different rates ?

A man invested an amount at 12 % per annum simple interest and another

1.	A man invested an amount at 12 % per annum simple interest and another amount at 10 % per annum simpel interest. He received an annual interest fo ₹ 2600. But, if he had intercharged the amounts invested, he would havr received ₹ 140 less. What amounts did he invest at the different rates ?
Answer» Let the amound invested at 12 % by ₹ x and that invested at 10 % be ₹ y . Then , total annual interest `" " = ₹ ((x xx 12 xx 1 )/( 100) + (y xx 10 xx 1)/(100)) = ₹ ((6x + 5y)/( 50))` ` therefore ( 6x + 5y )/( 50) = 2600 rArr 6x + 5y = 130000 " " `... (i) Again, the amount invested at 12 % is ₹ y and the invested at 10 % is ₹ x. Total annual interest at the new rates `" " = ₹(( yxx 12 xx 1)/( 100 ) + (x xx 10 xx 1 )/( 100)) = ₹ ((6y + 5x )/( 50))` But, interest received at the new rates = ₹ (2600- 140 ) = ₹ 2460. ` therefore ( 6y + 5x)/( 50 ) = 2460 rArr 5 x + 6y = 123000" " `... (ii) Adding (i) and (ii), we get ` 11 x + 11y = 253000 rArr 11 (x + y ) = 253000 ` ` rArr x + y = 23000" " `... (iii) Subtracting (ii) from (i), we get ` x - y = 7000 " " `...(iv) Adding (iii) and (iv), we get ` 2x = 30000 rArr x = 15000 ` Putting ` x = 15000 ` in (i) , we get `15000 + y = 23000 rArr y =23000 - 15000 = 8000` ` therefore x = 15000 and y = 8000` Hence, the amount at 12 % is ₹ 15000 and that at 10 % is ₹ 8000.

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A man invested an amount at 12 % per annum simple interest and another amount at 10 % per annum simpel interest. He received an annual interest fo ₹ 2600. But, if he had intercharged the amounts invested, he would havr received ₹ 140 less. What amounts did he invest at the different rates ?

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