What sum will produce the same interest in 9 years at the rate 8% simple interest as Rs 800 produce in 3 years at 9/2% per amum?
A. Rs. 100
B. Rs. 125
C. Rs 150
D. Rs. 110

Options

A. C
B. D
C. B
D. A

Answer

To solve the problem, we will use the formula for Simple Interest (SI):

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \(SI\) = Simple Interest
- \(P\) = Principal amount
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

### Step 1: Calculate the interest produced by Rs 800 in 3 years at 9/2% per annum.

Given:
- Principal \(P = 800\)
- Rate \(R = \frac{9}{2} = 4.5\%\)
- Time \(T = 3\) years

Using the formula:

\[ SI = \frac{800 \times 4.5 \times 3}{100} \]

Calculating the interest:

\[ SI = \frac{800 \times 4.5 \times 3}{100} = \frac{10800}{100} = 108 \]

### Step 2: Set up the equation for the unknown principal \(x\) that will produce the same interest in 9 years at 8%.

Now we need to find the principal \(x\) that will produce the same interest of Rs 108 in 9 years at 8% per annum.

Given:
- Rate \(R = 8\%\)
- Time \(T = 9\) years

Using the formula again:

\[ SI = \frac{x \times 8 \times 9}{100} \]

Setting this equal to the interest calculated in Step 1:

\[ \frac{x \times 8 \times 9}{100} = 108 \]

### Step 3: Solve for \(x\).

First, simplify the left side:

\[ \frac{72x}{100} = 108 \]

Now, multiply both sides by 100 to eliminate the fraction:

\[ 72x = 10800 \]

Next, divide both sides by 72:

\[ x = \frac{10800}{72} \]

Calculating \(x\):

\[ x = 150 \]

### Conclusion

The sum that will produce the same interest in 9 years at the rate of 8% simple interest is **Rs 150**.