If a certain sum of money doubles itself in 6 years, in how many years will it…

Step-by-Step Solution

To find the time required for a sum to triple itself under simple interest, we can analyze the growth of the interest earned.

1. Analyze the first scenario (doubling):

   • If a sum doubles, the Amount (A) becomes 2P (where P is the principal).

   • Simple Interest (SI) earned = Amount - Principal = 2P - P = P.

   • This interest (P) is earned in 6 years.

2. Analyze the second scenario (tripling):

   • To triple the sum, the Amount (A) must become 3P.

   • Simple Interest (SI) required = Amount - Principal = 3P - P = 2P.

3. Calculate the time required:

   • Since Simple Interest is directly proportional to time, we can set up a ratio:

   • (SI 1) / (Time 1) = (SI 2) / (Time 2)

   • P / 6 years = 2P / (Time 2)

   • Time 2 = (2P * 6 years) / P

   • Time 2 = 12 years.