Question

If a sum of money doubles itself but in 7 years, it becomes 5times in how many years

Answer 1

as the money doubles in every 7 years
after 17.5 years it will be 5 times

Answer 2

Let the sum of money be p

A = 2p in T = 7
A = 5p in T = ?

A = p(1 + r/100)^n

2p = p ( 1 + r/100)^7
2p/p = ( 1 + r/100)^7
(2)^1 = ( 1 + r/100)^7
(2)^1/7 = ( 1 + r/100) ..... Case 1

A=p(1+r/100)^n
5p = p(1 + r/100)^n
5p/p = (1 + r/100)^n
5 = ( (2)^1/7 )^n ....Executing Case 1
5 = ( 2 )^ n/7
(2)^2.5 = (2)^n/7. ( Comparing bases )
2.5 = n/7
n = 7× 2.5
n = 17.5 yrs

In 17.5 yrs the sum of money will become 5 times of itself

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