In a division sum, the divisor is $12$ times the quotient and $5$ times the remainder. If the remainder is $48$, then the dividend is

### Concept & Formula This problem requires a cascaded application of the Division Algorithm. We must use the given ratios and the single known numerical value to back-calculate all missing variables step-by-step. $$ \text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder} $$ ### Step-by-Step Solution * **Given:** * Remainder ($R$) = $48$ * Divisor ($D$) = $12 \times$ Quotient ($Q$) * Divisor ($D$) = $5 \times$ Remainder ($R$) * **Calculation:** * First, calculate the Divisor using the Remainder: * $D = 5 \times 48 = 240$ * Next, find the Quotient using the Divisor: * $240 = 12 \times Q$ * $Q = 240 / 12 = 20$ * Finally, use the standard formula to find the Dividend: * $\text{Dividend} = (D \times Q) + R$ * $\text{Dividend} = (240 \times 20) + 48$ * $\text{Dividend} = 4800 + 48 = 4848$ ### Exam Strategy & Shortcut Use modular arithmetic logic. The Dividend is $(240 \times 20) + 48$. Notice that $240 \times 20$ ends in $00$. Therefore, the last two digits of the dividend must exactly match the remainder, which is $48$. Only options (b) and (d) end in $48$. A quick mental estimate of $240 \times 20 = 4800$ immediately points to $4848$, bypassing full written calculation. ### Common Pitfall A common error is mixing up the multiplicative relationships (e.g., multiplying the remainder by $12$ instead of $5$). Carefully mapping out the "is" statements into equations ($D = 12Q$ and $D = 5R$) prevents this miscalculation. ### Final Answer Therefore, the correct answer is **4848**.