Ramu borrowed Rs35000 from Somu. A part of the sum is borrowed at 10% per annum under simple interest for 4 years and the remaining part at 11% per annum under simple interest for `(4)1/2` years. If the total interest earned by Somu is Rs15900, then find the sum borrowed at each rate.

Explanation

Let the sum borrowed by Ramu at 10% per annum be Rs. X. Then, the sum borrowed at 11% per annum =Rs. (35000-x)
Now, simple interest on the sum Rs.`X=(x xx 4xx10)/(100)`
Simple interest on the sum
`Rs. (35000-x)=((3500-x)xx(9)/(2)xx11)/(100)`
Given, the total interest earned = Rs. 15900
`therefore (40x)/(100)+((3500-x)xx(9)/(2)xx11)/(100)=15900`
`(80x+99(35000-x))/(200)=15900`
`implies 19x=99xx35000-15900xx200`
`implies x=(1000xx15(231-212))/(19)implies x =15000`
Hence, the sum borrowed at 10% per annum = Rs. 15000 and the sum borrowed at 11% per annum = Rs. 20000.