If an amount of ₹ 4,36,563 is distributed equally amongst 69 persons, how much amount would each person get?

### Concept & Strategy This is a straightforward division problem: $\frac{\text{Total Amount}}{\text{Total Persons}}$. However, since exam time is limited and long division of a 6-digit number by a 2-digit number is tedious, the optimal strategy relies on **Unit Digit Analysis** and **Approximation**. ### Step-by-Step Solution We need to calculate: $436563 \div 69$ **Step 1: Unit Digit Analysis** Look at the last digit of the total amount (3) and the last digit of the divisor (9). We are looking for a quotient $Q$ such that: $69 \times Q = 436563$. This means the unit digit of $Q$ multiplied by 9 must yield a number ending in 3. Let's check the multiples of 9: $9 \times 1 = 9$ $9 \times 2 = 18$ $9 \times 3 = 27$ $9 \times 7 = 63$ <-- Ends in 3! Therefore, the correct answer must end in the digit **7**. Look at the options provided: (a) 5876 (Ends in 6) (b) 5943 (Ends in 3) (c) 6148 (Ends in 8) (d) 6327 (Ends in 7) Option (d) is the only candidate that satisfies the unit digit requirement. **Step 2: Verification (Optional but recommended)** To be certain (since "None of these" is an option), verify if $6327 \times 69$ is near 436563 using approximation. Approximate $6327$ to $6300$ and $69$ to $70$. $6300 \times 70 = 441,000$. 441,000 is very close to 436,563, confirming our unit digit deduction is correct and not off by an order of magnitude. ### Exam Strategy & Shortcut **The $(10x - 1)$ Trick:** To perfectly verify $69 \times 6327$ mentally: Treat $69$ as $(70 - 1)$. $6327 \times (70 - 1)$ $= (6327 \times 70) - 6327$ $= 442890 - 6327 = 436563$. This perfectly matches the original number without doing full long multiplication. ### Common Pitfall Choosing to execute standard long division. While it will get you the right answer, dividing 436563 by 69 by hand takes at least 60-90 seconds and opens the door for subtraction errors. Unit digit analysis solves it in 5 seconds. ### Final Answer Therefore, the correct answer is **₹ 6327**.