Smita was asked to multiply a certain number by 36. She multiplied it by 63 instead and got an answer 3834 more than the correct one. What was the number to be multiplied?

### Concept & Formula This is an algebraic simplification problem based on linear equations. When a number is multiplied by an incorrect multiplier, the difference between the wrong answer and the right answer is proportional to the difference between the two multipliers. $$ \text{Difference in Product} = x \times (\text{Wrong Multiplier} - \text{Right Multiplier}) $$ ### Step-by-Step Solution * **Define the variable:** Let the unknown number to be multiplied be $x$. * **Formulate the equation based on given conditions:** Correct calculation should have been: $36x$ Incorrect calculation performed: $63x$ The problem states the incorrect answer is 3834 *more* than the correct one. $$ 63x - 36x = 3834 $$ * **Simplify the equation:** $$ (63 - 36)x = 3834 $$ $$ 27x = 3834 $$ * **Solve for x:** $$ x = \frac{3834}{27} $$ Divide by 9 first for easier arithmetic: $\frac{3834}{9} = 426$. Divide by 3: $\frac{426}{3} = 142$. ### Exam Strategy & Shortcut Skip straight to the difference in the multipliers. Difference in multipliers = $63 - 36 = 27$. The error (3834) is exactly 27 times the original number. Divide the error by the difference: $3834 / 27 = 142$. No need to write out the full algebraic equation. ### Common Pitfall Students often write the equation backward (e.g., $36x - 63x$) and get confused by a negative sign, or they attempt to guess and check the options, which consumes way too much time for a simple linear division. ### Final Answer **Therefore, the correct answer is 142.**