To solve this problem, let’s break it down step-by-step using the information provided:

1. Given Information:

   • A sum of money becomes four times itself in 10 years under simple interest.
   • We are asked to find in how many years the same sum of money will become three times itself at the same interest rate.

2. Setting Up the Problem:

   • Let the principal (initial sum) be $P$.
   • According to the problem, in 10 years, the amount becomes $4P$, which means the interest earned is $4P - P = 3P$.

3. Calculating the Rate of Interest:

   • Since simple interest $\text{SI} = P \times R \times T$ where $R$ is the rate per annum and $T$ is the time in years.
   • We know that $\text{SI} = 3P$ and $T = 10$ years, so: $3P = P \times R \times 10$
   • Dividing both sides by $P$ (assuming $P \neq 0$): $3 = R \times 10$
   • Solving for $R$: $R = \frac{3}{10} = 0.3 \text{ or } 30\%$

4. Finding the Time to Become Three Times Itself:

   • Now, we want the money to become three times itself, meaning the amount should be $3P$.
   • The interest earned in this case would be $3P - P = 2P$.
   • Using the simple interest formula again, we have: $2P = P \times 0.3 \times T$
   • Dividing both sides by $P$: $2 = 0.3 \times T$
   • Solving for $T$: $T = \frac{2}{0.3} = \frac{20}{3} = 6 \frac{2}{3} \text{ years}$

Answer: The money will become three times itself in $6 \frac{2}{3}$ years or approximately 6 years and 8 months.

Would you like more details or explanations on any part of this solution?

Related Questions:

1. What would the time be if the money had to become five times itself?
2. How would the solution change if compound interest was used instead?
3. Can you explain how to determine the rate of interest in more detail?
4. What is the formula for simple interest, and why is it applicable here?
5. How does changing the rate of interest affect the time taken for the sum to triple?

Tip:

For simple interest problems, remember that the interest grows linearly with time, which makes it easier to calculate for whole-number multiples of the principal.