Question

If the simple interest on a sum of money for 4 years at 8% per annum is Rs 1,920, find the principal.

• A. Rs 5,000
• B. Rs 6,000
• C. Rs 7,500
• D. Rs 8,000

Hint:

You can use effective percentage interest to solve this faster.
At 8% per annum for 4 years, the total simple interest accrued is $8\% \times 4 = 32\%$ of the principal.
We are given that $32\%$ of the Principal is equal to Rs 1,920.
So, $1\% = 1920 \div 32 = 60$.
The principal ($100\%$) is $60 \times 100 = 6000$ instantly.

Answer 1

The Correct Option is B

Step 1: Write the simple interest formula.
\[ SI = \frac{P \times R \times T}{100} \] where $P$ is the principal we want.

Step 2: Plug in the known values.
We know $SI = 1920$, $R = 8$, and $T = 4$. So \[ 1920 = \frac{P \times 8 \times 4}{100} \]

Step 3: Simplify the right side.
$8 \times 4 = 32$, so the equation is $1920 = \frac{32P}{100}$.

Step 4: Clear the fraction.
Multiply both sides by $100$, giving $192000 = 32P$.

Step 5: Solve for P.
Divide both sides by $32$, so $P = \frac{192000}{32} = 6000$.

Step 6: State the answer.
The principal was $6000$ rupees. \[ \boxed{\text{Rs } 6000} \]