Solve `10%` of `x+20%` of `y=24`
`3x-y=20`

Answer

To solve the simultaneous linear equations given by:

1. \( 10\% \text{ of } x + 20\% \text{ of } y = 24 \)
2. \( 3x - y = 20 \)

we will follow these steps:

### Step 1: Convert percentages to fractions
We start with the first equation:
\[ 10\% \text{ of } x + 20\% \text{ of } y = 24 \]
This can be rewritten as:
\[ \frac{10}{100}x + \frac{20}{100}y = 24 \]
Simplifying the fractions gives:
\[ \frac{1}{10}x + \frac{1}{5}y = 24 \]

### Step 2: Eliminate the fractions
To eliminate the fractions, we can multiply the entire equation by 10 (the least common multiple of the denominators):
\[ 10 \left(\frac{1}{10}x + \frac{1}{5}y\right) = 10 \cdot 24 \]
This simplifies to:
\[ x + 2y = 240 \]
Let’s call this Equation (1).

### Step 3: Write the second equation
The second equation is already given as:
\[ 3x - y = 20 \]
Let’s call this Equation (2).

### Step 4: Make the coefficients of \(y\) the same
To eliminate \(y\), we can multiply Equation (2) by 2:
\[ 2(3x - y) = 2 \cdot 20 \]
This simplifies to:
\[ 6x - 2y = 40 \]
Let’s call this Equation (3).

### Step 5: Add Equations (1) and (3)
Now we will add Equation (1) and Equation (3):
\[ (x + 2y) + (6x - 2y) = 240 + 40 \]
This simplifies to:
\[ 7x = 280 \]

### Step 6: Solve for \(x\)
Now, divide both sides by 7:
\[ x = \frac{280}{7} = 40 \]

### Step 7: Substitute \(x\) back to find \(y\)
Now that we have \(x\), we can substitute it back into Equation (1):
\[ 40 + 2y = 240 \]
Subtract 40 from both sides:
\[ 2y = 240 - 40 \]
This simplifies to:
\[ 2y = 200 \]
Now, divide both sides by 2:
\[ y = \frac{200}{2} = 100 \]

### Final Solution
Thus, the solution to the equations is:
\[ x = 40, \quad y = 100 \]