# Amal and Bimal invested some amount in a bank at an interest rate of 10%. Amal selected a plan in which interest amount calculated annually in simple

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Amal and Bimal invested some amount in a bank at an interest rate of 10%. Amal selected a plan in which interest amount calculated annually in simple method. In Bimal's plan interest calculated annually by the compound interest method. If both received the same interest amount after 2 years, what will be the ratio of investments made by Amal and Bimal?
1. 21 : 20
2. 11 : 10
3. 10 : 11
4. 20 : 21

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Correct Answer - Option 1 : 21 : 20

Calculation:

Let m and n are the investments by Amal and Bimal

Interest amount received by amal after 2 years = m × (r/100) × t

⇒ I = m × (10/100) × 2

⇒ I = 0.2m      ---(1)

Interest amount received by Bimal after 2 years = n ( 1 + (r/100))t  - n

⇒ I = n × ( 1 + (10/100))2 - n

⇒ I = 1.12n - n

⇒ I = 0.21n      ---(2)

(1) = (2)

⇒ 0.2m = 0.21n

m/n = 21/20

Make sure which amounts are equal, whether it is the total amount or the interest amount.