an investor received $1400 interest per annum from a sum of money, with part of it invested at 10% and the remainder at 7% simple interest. This investor found that if she interchanged the amounts she had invested she could increase her return by $90 per annum. Calculate the total amount invested.

Step-by-step explanation:

let x be one part of the money invested.

let y be the other part of the money invested.

x * (10/100) - - amount on 10% of interest per annum

y * (7/100) - amount invested on 7% of interest per annum

x * (10/100) + y * (7/100) = 1400

on simplifying it

10x + 7y = 140000 - - (1)

On interchanging the interest rate on x amount and y amount of the investor

x * (7/100) + y * (10/100) = 1490

7x + 10y = 149000 - (2)

on solving equation (1) and (2) we get

70x + 49y = 980000

70x + 100y = 1490000

-51y = - 510000

y=10000

and x=7000

So our total amount invested is 17000