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Question
A sum of money lent out at C.I. at a certain rate per annum becomes three times of itself in 10 years. Find in how many years will the money become twenty-seven times of itself at the same rate of interest p.a.
Solution
Let Principal be Rs y and rate= r%
According to 1st condition
Amount in 10 years = Rs 3y
∴ A = P`( 1 + r/100 )^n`
⇒ 3y = y `( 1 + r/100 )^10`
⇒ 3 =`( 1 + r/100 )^10` ...(1)
According to 2nd condition
Let after n years amount will be Rs 27y
∴ A = P`( 1 + r/100 )^n`
⇒ 27y = y `( 1 + r/100 )^n`
⇒ (3)^3 =`( 1 + r/100 )^n`
Put value from first equation
⇒ `[( 1 + r/100 )^10]^3 = ( 1 + r/100)^n`
On comparing, we get
n = 10 x 3 = 30 years
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