Question

tek invests $6000 , done at 3%, the rest at 2%. his total interest is $160. how much is invested at each rate?

Answer 1

$4,000 is invested at 3%

Amount $2000 is invested at 2%.

Explanation:

Here, the given total Principal Amount = $6000

Let us assume the amount M is invested at 3%

Let us amuse the amount is invested for 1 year.

So, the remaining amount ( $6000 - M) is invested at the rate 2%.

Now, SIMPLE INTEREST =
`(P * R * T)/(100)`

CASE 1: when Amount M is invested

Simple Interest =
`(M * 3 * 1)/(100)` =
`(3M)/(100)  = 0.03M`

or, SI = 0.03 M

CASE 2: when Amount ( $6000 - M) is invested

Simple Interest =
`((6000 - M) * 2 * 1)/(100)` =
`((2* 6000 - 2M)/(100)  = 120 - 0.02M`

or, SI = (120 - 0.02 M)

Now, total simple interest received = $160.

⇒ 0.03 M + (120 - 0.02 M) = 160

⇒ 0.03 M + 120 - 0.02 M = 160

or, 0.01 M = 40

⇒ M = 40 / 0.01 = 4,000

or, M = 4,000

Hence, $4,000 is invested at 3%

and the amount (6000 - 4000) = $2000 is invested at 2%.