# Ram invested a certain amount of money in a bank. The interest amount calculated annually by the simple method. For the first two years, the interest

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Ram invested a certain amount of money in a bank. The interest amount calculated annually by the simple method. For the first two years, the interest rate is 8% and after that, the interest rate is 10%. If his investment was for seven years, what will be the ratio of the total interest amount he received in the first five years to the last five years?
1. 23 : 25
2. 4 : 5
3. 17 : 20
4. 21 : 25

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Correct Answer - Option 1 : 23 : 25

Calculation:

Here the first two-year interest rate of 8% and then 10%.

⇒ After 5 years = P × (8/100) × 2 + P × (10/100) × 3 = 0.16P + 0.3P = 0.46P

Investment is for 7 years.

∴ last 5 years interest amount ⇒  the interest amount received form year 3 to year 7.

⇒ Interest = P × (10/100) × 5 = 0.5P

Ratio is 0.46P : 0.5P ⇒  23 : 25

If the interest amount changing after some time, you cant apply the standard equation straight away. Find the interest by splitting into periods where the interest rate is the same is throughout the period.

Here you can take the principal amount as P or 100.BUt if there are related questions it is better to take investment as P.