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

Answer:

$4,000 is invested at 3%

Amount   $2000 is invested at 2%.

Step-by-step 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  = $\frac{P \times R \times T}{100}$

CASE 1: when Amount M is invested

Simple Interest = $\frac{M \times 3 \times 1}{100}$  = $\frac{3M}{100} = 0.03M$

or, SI = 0.03 M  

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

Simple Interest = $\frac{(6000 - M) \times 2 \times 1}{100}$  = $\frac{(2\times 6000 - 2M}{100} = 120 - 0.02M$

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%.