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.

Answer 1

Let Principal be Rs y and rate= r%
According to 1^st 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 2^nd 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