Question

A sum of Rs. 800 amounts to Rs. 920 in 3 years at simple interest. What would be the amount, if the interest rate is increased by 3%?

• A. Rs. 800
• B. Rs. 192
• C. Rs. 992
• D. Rs. 120

Hint:

Remember the simple interest formula: \( SI = \frac{P \times R \times T}{100} \). When the interest rate changes, calculate the new interest based on the original principal and time.

Answer 1

The Correct Option is C

Step 1: Calculate the initial simple interest.
Initial Simple Interest (SI) = Amount - Principal = \rupee 920 - \rupee 800 = \rupee 120 

Step 2: Calculate the initial rate of interest (R).
Using the formula for simple interest: \( SI = \frac{P \times R \times T}{100} \), where P is the principal, R is the rate of interest, and T is the time.
$$120 = \frac{800 \times R \times 3}{100}$$
$$120 = 24 R$$
$$R = \frac{120}{24} = 5\%$$


Step 3: Calculate the new rate of interest.
The interest rate is increased by 3\%, so the new rate \( R = R + 3\% = 5\% + 3\% = 8\% \) 

Step 4: Calculate the new simple interest.
Using the new rate of interest:
$$SI = \frac{P \times R \times T}{100} = \frac{800 \times 8 \times 3}{100} = \frac{19200}{100} = \rupee 192$$
Step 5: Calculate the new amount.
New Amount = Principal + New Simple Interest = \( \rupee 800 + \rupee 192 = \rupee 992 \)