Abhishek invested a certain some at the rate of certain interest rate. If he had invested at the rate of 4% more then he would have got Rs 800 more. Find the investment?

Options

A. 8000
B. 6000
C. 5000
D. 4000

Answer

To solve the problem, we need to use the formula for Simple Interest (SI), which is given by:

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

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

### Step 1: Set up the equations

Let:
- \(P\) = Principal amount (the investment)
- \(R\) = Original rate of interest
- \(T\) = Time period (in years)

From the problem, we know that if the rate of interest is increased by 4%, the interest earned would increase by Rs 800.

1. The interest earned at the original rate \(R\) for time \(T\) is:
\[ SI_1 = \frac{P \times R \times T}{100} \]

2. The interest earned at the increased rate \(R + 4\%\) for the same time \(T\) is:
\[ SI_2 = \frac{P \times (R + 4) \times T}{100} \]

According to the problem, the difference between these two interests is Rs 800:
\[ SI_2 - SI_1 = 800 \]

### Step 2: Substitute the equations

Substituting the expressions for \(SI_1\) and \(SI_2\) into the equation gives:
\[ \frac{P \times (R + 4) \times T}{100} - \frac{P \times R \times T}{100} = 800 \]

### Step 3: Simplify the equation

Now, simplify the left side:
\[ \frac{P \times (R + 4 - R) \times T}{100} = 800 \]
\[ \frac{P \times 4 \times T}{100} = 800 \]

### Step 4: Solve for \(P\)

Now, we can solve for \(P\):
\[ P \times 4 \times T = 800 \times 100 \]
\[ P \times 4 \times T = 80000 \]
\[ P = \frac{80000}{4T} \]
\[ P = \frac{20000}{T} \]

### Step 5: Conclusion

The investment \(P\) depends on the time \(T\). Without knowing the time period, we cannot find a specific numerical value for \(P\). However, we can express the investment in terms of \(T\):
\[ P = \frac{20000}{T} \]