In this question, we are given that a sum triples in ten years under compound interest at a certain rate. We need to find out in how many years the sum will become nine times.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal amount (initial sum)

r = the annual interest rate (in decimal form)

n = the number of times that interest is compounded per year

t = the number of years

Given that the sum triples in ten years, we can write the equation:

3P = P(1 + r/1)^(1*10)

Simplifying this equation, we get:

3 = (1 + r)^10

To find out when the sum becomes nine times, we can set up the equation:

9P = P(1 + r/1)^(1*t)

Simplifying this equation, we get:

9 = (1 + r)^t

Comparing the two equations, we can see that we need to find the value of t such that (1 + r)^t = 9.

Solving this equation, we find that t = 20.

Therefore,