What will come in place of (?) in the following questions ?
`((? + 65)/(45%"of 480")) xx 72 div 35 xx 840 = ? xx 18`

Options

A. 13
B. 65
C. 52
D. 26

Answer

To solve the equation \(\frac{(? + 65)}{(45\% \text{ of } 480)} \times 72 \div 35 \times 840 = ? \times 18\), we will follow a systematic approach.

### Step-by-Step Solution:

1. **Calculate 45% of 480**:
\[ 45\% \text{ of } 480 = \frac{45}{100} \times 480 = \frac{45 \times 480}{100} \]
Simplifying this:
\[ = \frac{21600}{100} = 216 \]

2. **Rewrite the equation**:
Now substitute \(216\) back into the equation:
\[ \frac{(? + 65)}{216} \times 72 \div 35 \times 840 = ? \times 18 \]

3. **Simplify the left side**:
First, calculate \(72 \div 35\):
\[ 72 \div 35 = \frac{72}{35} \]
Now, multiply by \(840\):
\[ \frac{72 \times 840}{35} \]
Simplifying \(840 \div 35\):
\[ 840 \div 35 = 24 \]
So, we have:
\[ 72 \times 24 = 1728 \]

4. **Rewrite the equation again**:
The equation now looks like:
\[ \frac{(? + 65)}{216} \times 1728 = ? \times 18 \]

5. **Multiply both sides by 216**:
\[ (? + 65) \times 1728 = ? \times 18 \times 216 \]

6. **Calculate \(18 \times 216\)**:
\[ 18 \times 216 = 3888 \]
So the equation becomes:
\[ (? + 65) \times 1728 = ? \times 3888 \]

7. **Distribute and rearrange**:
\[ 1728? + 1728 \times 65 = 3888? \]
Rearranging gives:
\[ 1728? - 3888? = -1728 \times 65 \]
\[ -2160? = -1728 \times 65 \]

8. **Divide both sides by -2160**:
\[ ? = \frac{1728 \times 65}{2160} \]

9. **Calculate \(1728 \div 2160\)**:
Simplifying:
\[ = \frac{1728}{2160} = \frac{72}{90} = \frac{4}{5} \]
Now multiply by \(65\):
\[ ? = \frac{4}{5} \times 65 = 52 \]

### Final Answer:
Thus, the value that comes in place of (?) is \(52\).