The simple interest on a sum of Rs 1550 for 2 yrs is Rs 20 more than the simple interest on Rs 1450 for the same duration (the rate of interest is the same in both the cases). Find the rate of interest.

10%

The correct answer is Option (2) → 10%

To find the rate of interest, we can use the formula for Simple Interest ($SI = \frac{P \times R \times T}{100}$).

Step 1: Set up the given information

• Principal 1 ($P_1$): Rs $1550$
• Principal 2 ($P_2$): Rs $1450$
• Time ($T$): $2$ years
• Difference in Interest ($SI_1 - SI_2$): Rs $20$
• Rate of Interest ($R$): $R\%$ (Same for both)

Step 2: Formulate the equation

The difference in simple interest is given by:

$\frac{P_1 \times R \times T}{100} - \frac{P_2 \times R \times T}{100} = 20$

We can factor out the common terms ($\frac{R \times T}{100}$):

$\frac{R \times T}{100} \times (P_1 - P_2) = 20$$

Step 3: Substitute the values and solve for $R$

$\frac{R \times 2}{100} \times (1550 - 1450) = 20$

$\frac{R \times 2}{100} \times 100 = 20$

Simplifying the equation:

$2R = 20$

$R = \frac{20}{2}$

$R = 10\%$

Final Answer: The rate of interest is $10\%$.