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A man in his deathbed fixed all his savings for his 3 children in 3 different schemes in such a way that each scheme will pay the respective child at their age of 18. His son, who is 15 years old gets 40%, elder daughter, who is 14 years old got 35% and younger daughter, who is 12 years old got the rest. If all of them got the same interest at their age of 18, what is the ratio of the rate of interest of those 3 schemes? (Assume all the schemes pay in simple interest)

A man in his deathbed fixed all his savings for his 3 children in 3 different schemes in such a way that each scheme will pay the respective child at their age of 18. His son, who is 15 years old gets 40%, elder daughter, who is 14 years old got 35% and younger daughter, who is 12 years old got the rest. If all of them got the same interest at their age of 18, what is the ratio of the rate of interest of those 3 schemes? (Assume all the schemes pay in simple interest) Correct Answer 35 : 30 : 28

Given:

Son got 40% of his total savings and he got the interest for 3 years.

Elder daughter got 35% of his total savings and she got the interest for 4 years.

Younger daughter got 25% of his total savings and she got the interest for 6 years.

Formula Used:

I = (P × t × r)/100

Where, P = Principle, t = time of investment, r = rate of interest

Calculations:

Let’s assume the rate of interest for son’s scheme is r1%, elder daughter’s scheme is r2% and younger daughter’s scheme is r3% and investment principle for them is 40x, 35x, 25x respectively.

Ratio of their interests

= 40x × 3 × r1 : 35x × 4 × r2 : 25x × 6 × r3

= 12 × r1 : 14 × r2 : 15 × r3

⇒ r1 : r2 : r3 = 35 : 30 : 28

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Ratio of their interest rates will be inverse of the ratio of multiplication of principle and time of investment.

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