Directions: These questions are based on the following information: $CBA + CCA = ACD$, where $A$, $B$, $C$ and $D$ stand for distinct digits and $D = 0$. $B$ takes the value

### Concept & Logic This is a cryptarithm addition puzzle. To solve it, align the numbers vertically and analyze the sum column by column (Units, Tens, Hundreds), tracking any carry-overs. The critical constraint here is that all letters represent *distinct* single digits from $0$ to $9$. ### Step-by-Step Solution * **Given:** $C B A$ $+ C C A$ $-------$ $A C D$ We are also given $D = 0$ and $A, B, C, D$ are distinct. * **Units Column:** $A + A = D$. Since $D = 0$, $A + A$ must end in $0$. This gives two possibilities for $A$: Case 1: $A = 0$. (But we know $D = 0$, and digits must be distinct. So $A \neq 0$). Case 2: $A = 5$. ($5 + 5 = 10$. We write $0$ for $D$ and carry over $1$ to the tens column). Therefore, $A = 5$. * **Tens Column:** $1 \text{ (carry)} + B + C = C$. This equation means that adding $(1 + B)$ to $C$ results in a number ending in $C$. For this to happen, the added amount $(1 + B)$ must be exactly $10$ (which generates a carry for the hundreds column without changing the unit digit $C$). $$1 + B = 10 \implies B = 9$$ ### Exam Strategy & Shortcut **Deduction by Substitution:** Once you find $A = 5$ from the units column, look immediately at the tens column: $B + C$. The result at the bottom is $C$. The only way a number added to $C$ results in $C$ again is if you are adding $0$ (which is impossible here due to the carry from the units place) or $10$. Since there is a carry of $1$, the equation is $1 + B = 10 \implies B = 9$. This takes seconds to spot without writing out complex algebra. ### Common Pitfall Forgetting the "distinct digits" rule is the most common error. If you forget this, you might incorrectly assume $A = 0$ in the first step (since $0 + 0 = 0$), which ruins the entire calculation. Always write down the constraints first. ### Final Answer Therefore, the correct answer is **9**.