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 = [tex]\frac{P \times R \times T}{100}[/tex]
CASE 1: when Amount M is invested
Simple Interest = [tex]\frac{M \times 3 \times 1}{100}[/tex] = [tex]\frac{3M}{100} = 0.03M[/tex]
or, SI = 0.03 M
CASE 2: when Amount ( $6000 - M) is invested
Simple Interest = [tex]\frac{(6000 - M) \times 2 \times 1}{100}[/tex] = [tex]\frac{(2\times 6000 - 2M}{100} = 120 - 0.02M[/tex]
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%.
