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Question
A certain sum of money becomes three times itself in 20 years at simple interest. In how many years does it become double of itself at the same rate of simple interest?
Solution
Given that, the sum of money triples itself in 20 years
∴ P + I = 3P
∴ I = 2P
and T = 20 years
Now simple interest I = `"PRT"/100`
∴ 2P = `("P" xx "R" xx 20)/100`
∴ R = 10
∴ Rate of interest = 10% per annum
The time period is to be calculated for the condition that the sum doubles itself i.e. for the condition
P + I = 2P
i.e. I = P
i.e. `("P" xx "R" xx "T")/100 = "P"`
∴ `(10 xx "T")/100 = 1`
∴ T = 10
∴ The sum will become double of itself in 10 years.
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