$10531 + 4813 - 728 = x \times 87$

### Concept & Strategy This question tests standard simplification rules combined with algebraic isolation. You must first resolve the complex arithmetic on the left-hand side (LHS) of the equation before dividing by the coefficient on the right-hand side (RHS). $$ \text{If } A + B - C = x \times D, \text{ then } x = \frac{A + B - C}{D} $$ ### Step-by-Step Solution * **Given:** The equation $10531 + 4813 - 728 = x \times 87$. * **Step 1:** Add the positive terms on the left side. $10531 + 4813 = 15344$ * **Step 2:** Subtract the negative term from the sum. $15344 - 728 = 14616$ * **Step 3:** Substitute the simplified LHS back into the equation. $14616 = x \times 87$ * **Step 4:** Isolate $x$ by dividing the LHS by $87$. $x = \frac{14616}{87}$ * **Step 5:** Perform the division (or use the shortcut below to avoid long division). $x = 168$ ### Exam Strategy & Shortcut **Unit Digit Analysis** is the fastest way to crack this. 1. Look at the unit digits on the left side: $1 + 3 - 8 \rightarrow 4 - 8$. Since we can't subtract $8$ from $4$, borrow a $1$ (making it $14$). $14 - 8 = 6$. So, the entire left side resolves to a number ending in $6$. 2. Look at the right side: $x \times 87$. The unit digit of $x$ multiplied by $7$ must yield a number ending in $6$. What times $7$ ends in $6$? Only $8$ ($8 \times 7 = 56$). 3. Check the options. Only option (a) $168$ ends in $8$. You can confidently mark it without performing the $14616 \div 87$ long division. ### Common Pitfall The most common mistake is attempting the long division ($14616 \div 87$) under time pressure, which often leads to arithmetic errors and wastes precious minutes. Always look for unit digit shortcuts before doing heavy division. ### Final Answer Therefore, the correct answer is **168**.