If `x=(-23)+22+(-23)+22…………..` (40 terms) and `y=11+(-10)+11+(-10)+….` (20 terms) then `y-x` is ___________.

Options

A. 40
B. 10
C. 20
D. `30`

Answer

To solve the problem, we need to calculate the values of \( x \) and \( y \) separately and then find \( y - x \).

### Step 1: Calculate \( x \)

The expression for \( x \) is:
\[ x = (-23) + 22 + (-23) + 22 + \ldots \text{ (40 terms)} \]

We can group the terms in pairs:
\[ (-23 + 22) + (-23 + 22) + \ldots \]
Each pair sums to:
\[ -23 + 22 = -1 \]

Since there are 40 terms, we can find the number of pairs:
\[ \text{Number of pairs} = \frac{40}{2} = 20 \]

Now, we can calculate the total sum:
\[ x = 20 \times (-1) = -20 \]

### Step 2: Calculate \( y \)

The expression for \( y \) is:
\[ y = 11 + (-10) + 11 + (-10) + \ldots \text{ (20 terms)} \]

Again, we can group the terms in pairs:
\[ (11 + (-10)) + (11 + (-10)) + \ldots \]
Each pair sums to:
\[ 11 - 10 = 1 \]

Since there are 20 terms, we can find the number of pairs:
\[ \text{Number of pairs} = \frac{20}{2} = 10 \]

Now, we can calculate the total sum:
\[ y = 10 \times 1 = 10 \]

### Step 3: Calculate \( y - x \)

Now that we have both \( y \) and \( x \):
\[ y - x = 10 - (-20) \]
This simplifies to:
\[ y - x = 10 + 20 = 30 \]

### Final Answer
Thus, the value of \( y - x \) is:
\[ \boxed{30} \]

---