# How to solve this confusing Simple interest problem?

#### Ganesh Ujwal

A sum of Rs 3,974 is lent to at SI at a rate which makes it 5 1/2 times of itself in 9 years. What will be the ratio of final amount. When the same amount is put at SI for 13 years and 17 years respectively?

Ans: 15:19

#### Denis

Math Team
A sum of Rs 3,974 is lent to at SI at a rate which makes it 5 1/2 times of itself in 9 years. What will be the ratio of final amount. When the same amount is put at SI for 13 years and 17 years respectively?
Re-wording in proper English:
An amount of 3,974 is lent at Simple Interest at a rate
which makes that amount 5 1/2 times of itself in 9 years.
What will be the ratio of final amounts when the same
amount earns the same rate for 13 years and 17 years?

3974 * 5.5 = 21857 (value after 9 years)

(21857 - 3974) / 9 = 1987 (annual interest amount)

3974 + 1987 * 13 = 29805 (value after 13 years)

3974 + 1987 * 17 = 37753 (value after 17 years)

Resulting ratio = 29805 / 37753 = ?

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#### skipjack

Forum Staff
If the question was asking for the ratio (of each final amount) to the original amount, those ratios would be 29805/3974 and 37753/3974, which simply to 7 1/2 and 9 1/2 respectively.

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