A number when divided by $195$ leaves a remainder $47$. If the same number is divided by $15$, the remainder will be

### Concept & Rule This relies on the transitive property of divisibility. If a large block (the original divisor) can be perfectly broken down into smaller blocks (the new divisor), you only need to evaluate the "leftover" pieces (the original remainder) to find the final remainder. $$ \text{New Remainder} = \text{Old Remainder} \pmod{\text{New Divisor}} $$ ### Step-by-Step Solution * **Given:** * First Divisor = $195$ * First Remainder = $47$ * Second Divisor = $15$ * **Calculation:** * Step 1: Confirm that $195$ is a multiple of $15$. * $15 \times 10 = 150$, and $15 \times 3 = 45$. $150 + 45 = 195$. Yes, it divides perfectly. * Step 2: Since the base divisor is compatible, divide the original remainder by the new divisor. * Divide $47$ by $15$. * $15 \times 3 = 45$. * $47 - 45 = 2$. * The new remainder is $2$. ### Exam Strategy & Shortcut Bypass verifying the first divisor if you are severely short on time. In $99\%$ of competitive exam questions formatted exactly like this, the first divisor is deliberately designed to be a multiple of the second. Jump straight to dividing the old remainder by the new divisor: $47 / 15 \rightarrow$ remainder is $2$. ### Common Pitfall A fatal error occurs if a student divides the first divisor ($195$) by the new divisor ($15$), gets a quotient of $13$, and mistakenly marks a derivation of $13$ as the answer. Always focus operations strictly on the *remainder* once divisibility is confirmed. ### Final Answer Therefore, the correct answer is **2**.