Question

A total of ₹ 8,600 was invested in two accounts. One account earned `4 3/4`% annual interest and the other earned `6 1/2`% annual interest. If the total interest for one year was ₹ 431.25, how much was invested in each account? (Use determinant method)

Answer 1

Let ₹ x and ₹ y be the amounts invested in the two accounts.

Interest or first account = `4 3/4`% x

= `19/4 xx 1/100 xx x = 19/100 x`

Interest for second ccount = `6 1/2`%

= `13/2 xx /100` y

= `13/200` y

According to the problem,

x + y = 8600

`19/400 x + 13/200 y` = 431.25

Multiplying the second equation by 400,

19x + 26y = 172500

Here `Delta = |(1, 1),(19, 26)|`

= 26 – 19

= 7 ≠ 0

So the system has a unique solution

`Delta_x = |(8600, 1),(172500, 26)|`

= 223600 – 172500

= 51100

`Delta_y = |(1, 8600),(19, 172500)|`

= 172500 – 163400

= 9100

∴ By Cramer's rule,

x = `Delta_x/Delta = 51100/7` = 7300

y = `Delta_y/Delta = 9100/7` = 1300

Hence the amount invested at `4 3/4`% is ₹ 7300 and amount invested at `6 1/2`% is ₹ 1300.