In doing a question of division with zero remainder, a candidate took $12$ as divisor instead of $21$. The quotient obtained by him was $35$. The correct quotient is

### Concept & Formula When a remainder is zero, the Dividend is simply the product of the Divisor and the Quotient. If the divisor is misread, the underlying Dividend itself does not change; it remains a constant anchor we can use to find the correct quotient. $$ \text{Dividend} = \text{Divisor} \times \text{Quotient} $$ ### Step-by-Step Solution * **Given:** * Remainder = $0$ * Incorrect Divisor = $12$ * Incorrect Quotient = $35$ * Correct Divisor = $21$ * **Calculation:** * First, deduce the constant Dividend based on the candidate's incorrect reading: * $\text{Dividend} = 12 \times 35$ * $\text{Dividend} = 420$ * Now, recalculate using the correct Divisor to find the true Quotient: * Correct Quotient = Dividend / Correct Divisor * Correct Quotient = $420 / 21$ * Correct Quotient = $20$ ### Exam Strategy & Shortcut Since the Dividend is constant, you can set up an inverse proportion equation directly: $D_1 \times Q_1 = D_2 \times Q_2$ $12 \times 35 = 21 \times Q_2$ Simplify the ratio before multiplying: $Q_2 = (12 \times 35) / 21$. Divide $35$ and $21$ by their common factor $7$ to get $5$ and $3$. Then divide $12$ by $3$ to get $4$. Finally, $4 \times 5 = 20$. This avoids large multiplications entirely. ### Common Pitfall Calculating $12 \times 35$ manually can lead to arithmetic errors under time pressure. Delay multiplication until the final step. Setting it up as a fraction $(12 \times 35) / 21$ allows for rapid cross-cancellation. ### Final Answer Therefore, the correct answer is **20**.