Difference between `50%` of y and `10%` of x is 170 whereas difference between `40%` of x and `30%` of y is zero. Find the sum of 'x' and 'y' ?

Options

A. A)770
B. B)630
C. C)600
D. D)700

Answer

To solve the problem, we need to set up equations based on the information provided.

### Step 1: Set up the equations
We have two conditions given in the problem:

1. The difference between `50%` of `y` and `10%` of `x` is `170`.
2. The difference between `40%` of `x` and `30%` of `y` is `0`.

From the first condition, we can write the equation:
\[ \frac{50}{100}y - \frac{10}{100}x = 170 \]
This simplifies to:
\[ 0.5y - 0.1x = 170 \quad \text{(Equation 1)} \]

From the second condition, since the difference is `0`, we can write:
\[ \frac{40}{100}x - \frac{30}{100}y = 0 \]
This simplifies to:
\[ 0.4x - 0.3y = 0 \quad \text{(Equation 2)} \]

### Step 2: Solve Equation 2 for one variable
From Equation 2, we can express `x` in terms of `y`:
\[ 0.4x = 0.3y \]
Dividing both sides by `0.4` gives:
\[ x = \frac{0.3}{0.4}y = \frac{3}{4}y \]

### Step 3: Substitute `x` in Equation 1
Now, we substitute `x` in Equation 1:
\[ 0.5y - 0.1\left(\frac{3}{4}y\right) = 170 \]
This simplifies to:
\[ 0.5y - 0.075y = 170 \]
Combining like terms gives:
\[ 0.425y = 170 \]

### Step 4: Solve for `y`
To find `y`, divide both sides by `0.425`:
\[ y = \frac{170}{0.425} = 400 \]

### Step 5: Find `x`
Now, substitute `y` back into the equation for `x`:
\[ x = \frac{3}{4}y = \frac{3}{4} \times 400 = 300 \]

### Step 6: Find the sum of `x` and `y`
Now, we can find the sum of `x` and `y`:
\[ x + y = 300 + 400 = 700 \]

### Final Answer
The sum of `x` and `y` is:
\[ \boxed{700} \]