'A' invested Rs. X in a scheme on simple interest at the rate of 20% p.a. for two years and 'B' invested Rs. Y in same scheme. If interest got by A is Rs. 480 more than that of B after two years. If X is 25% more than Y, then find value sum of amount invested by A & B?

Options

A. 11400 Rs.
B. 10800 Rs.
C. 10200 Rs.
D. 10400 Rs.

Answer

To solve the problem step by step, we will follow the given information and apply the formulas for simple interest.

### Step 1: Understand the relationship between X and Y
We know that:
- \( X \) is 25% more than \( Y \).

This can be expressed mathematically as:
\[ X = Y + 0.25Y = 1.25Y \]

### Step 2: Set up the equation for the simple interest
The formula for simple interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

For A:
- Principal = \( X \)
- Rate = 20%
- Time = 2 years

So, the interest for A (SI_A) is:
\[ SI_A = \frac{X \times 20 \times 2}{100} = \frac{40X}{100} = 0.4X \]

For B:
- Principal = \( Y \)
- Rate = 20%
- Time = 2 years

So, the interest for B (SI_B) is:
\[ SI_B = \frac{Y \times 20 \times 2}{100} = \frac{40Y}{100} = 0.4Y \]

### Step 3: Set up the equation based on the difference in interest
According to the problem, the interest earned by A is Rs. 480 more than that earned by B:
\[ SI_A = SI_B + 480 \]
Substituting the expressions for SI_A and SI_B:
\[ 0.4X = 0.4Y + 480 \]

### Step 4: Substitute the value of X in terms of Y
From Step 1, we have \( X = 1.25Y \). Substitute this into the equation:
\[ 0.4(1.25Y) = 0.4Y + 480 \]
This simplifies to:
\[ 0.5Y = 0.4Y + 480 \]

### Step 5: Solve for Y
Subtract \( 0.4Y \) from both sides:
\[ 0.5Y - 0.4Y = 480 \]
\[ 0.1Y = 480 \]
Now, divide both sides by 0.1:
\[ Y = \frac{480}{0.1} = 4800 \]

### Step 6: Find the value of X
Now that we have \( Y \), we can find \( X \):
\[ X = 1.25Y = 1.25 \times 4800 = 6000 \]

### Step 7: Calculate the total investment
The total amount invested by A and B is:
\[ X + Y = 6000 + 4800 = 10800 \]

### Final Answer
The sum of the amounts invested by A and B is Rs. 10,800.

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