In a certain time, a sum becomes 3 times at the rate of 10% per annum (simple interest). At what rate per annum (simple ' interest), the same sum becomes 6 times in same duration ?

Given:

In a certain time, a sum becomes 3 times at the rate of 10% per annum (simple interest).

Formula used:

Simple Interest (SI) = \(P \times \dfrac{r \times t}{100}\)

Amount (A) = Principal (P) + Simple Interest (SI)

Calculation:

Let Principal = P

Final Amount = 3P

Simple Interest = 3P - P = 2P

Using the formula for Simple Interest:

\(SI = P \times \dfrac{r \times t}{100}\)

⇒ \(2P = P \times \dfrac{10 \times t}{100}\)

⇒ \(2 = \dfrac{10t}{100}\)

⇒ \(t = 20\)

Now, for the sum to become 6 times:

Final Amount = 6P

Simple Interest = 6P - P = 5P

Using the formula for Simple Interest:

\(SI = P \times \dfrac{r \times t}{100}\)

⇒ \(5P = P \times \dfrac{r \times 20}{100}\)

⇒ \(5 = \dfrac{20r}{100}\)

⇒ r = 25%

∴ The correct answer is option (1).