Difference between `40%` of y and `20%` of x is 270 whereas difference between `40%` of x and `20%` of y is zero. Find the sum of 'x' and 'y' ?

Options

A. A)1250
B. B)1400
C. C)1200
D. D)1350

Answer

To solve the problem step by step, we will break down the information given in the question and use it to find the values of \( x \) and \( y \).

### Step 1: Set up the equations based on the problem statement.

We know from the problem:

1. The difference between \( 40\% \) of \( y \) and \( 20\% \) of \( x \) is \( 270 \):
\[ 0.4y - 0.2x = 270 \quad \text{(Equation 1)} \]

2. The difference between \( 40\% \) of \( x \) and \( 20\% \) of \( y \) is \( 0 \):
\[ 0.4x - 0.2y = 0 \quad \text{(Equation 2)} \]

### Step 2: Simplify Equation 2.

From Equation 2:
\[ 0.4x = 0.2y \]
Dividing both sides by \( 0.2 \):
\[ 2x = y \quad \text{(Equation 3)} \]

### Step 3: Substitute Equation 3 into Equation 1.

Now, substitute \( y \) from Equation 3 into Equation 1:
\[ 0.4(2x) - 0.2x = 270 \]
This simplifies to:
\[ 0.8x - 0.2x = 270 \]
Combining like terms:
\[ 0.6x = 270 \]

### Step 4: Solve for \( x \).

Now, divide both sides by \( 0.6 \):
\[ x = \frac{270}{0.6} = 450 \]

### Step 5: Find \( y \) using Equation 3.

Now that we have \( x \), we can find \( y \):
\[ y = 2x = 2 \times 450 = 900 \]

### Step 6: Find the sum of \( x \) and \( y \).

Now, we can find the sum of \( x \) and \( y \):
\[ x + y = 450 + 900 = 1350 \]

### Final Answer:
The sum of \( x \) and \( y \) is \( 1350 \).

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