In what time will the simple interest on ₹2200 at 6% per annum be the same as that on ₹1650 at 9% per annum in 10 years?

11 years and 3 months

The correct answer is Option (1) → 11 years and 3 months

1. Calculate Simple Interest for the Second Case

The formula for Simple Interest ($SI$) is:

$SI = \frac{P \times R \times T}{100}$

For the second case:

• Principal ($P_2$) = ₹1650
• Rate ($R_2$) = 9% per annum
• Time ($T_2$) = 10 years

$SI_2 = \frac{1650 \times 9 \times 10}{100} = 165 \times 9 = ₹1485$

2. Calculate the Time for the First Case

We are told that the interest for the first case ($SI_1$) is the same as the second case ($SI_2 = ₹1485$).

For the first case:

• Principal ($P_1$) = ₹2200
• Rate ($R_1$) = 6% per annum
• Interest ($SI_1$) = ₹1485
• Time ($T_1$) = ?

Using the formula rearranged for Time:

$T = \frac{SI \times 100}{P \times R}$

$T_1 = \frac{1485 \times 100}{2200 \times 6}$

$T_1 = \frac{1485}{22 \times 6} = \frac{1485}{132}$

$T_1 = 11.25 \text{ years}$

3. Convert Decimal Years to Months

• $11.25 \text{ years} = 11 \text{ years} + 0.25 \text{ years}$
• $0.25 \times 12 \text{ months} = 3 \text{ months}$

Final Answer:

The time taken will be 11 years and 3 months.