If a certain sum of money becomes 49 times of itself in 17 years. In how many years it will become 343 times of it self?

25.5 years

Let the sum = P

ATQ,

49P = P(1 + \(\frac{R}{100}\))¹⁷ .... (i)

343P = P(1 + \(\frac{R}{100}\))^T 

from eq. (i) ⇒

(49)^{\(\frac{1}{17}\)} = (1 + \(\frac{R}{100}\))

343 = (49)^{\(\frac{T}{17}\)} 

7³ = (7²)^{\(\frac{T}{17}\)} 

7³ = (7)^{\(\frac{2T}{17}\)}  ⇒  \(\frac{2T}{17}\) = 3

T = \(\frac{51}{2}\) = 25.5 years