Sweets were distributed equally among 64 children. After giving 7 sweets to each child 15 sweets were left out. Total how many sweets were there?

### Concept & Logic This is a basic arithmetic problem involving multiplication and addition to find an original total quantity from distributed amounts and a remainder. ### Step-by-Step Solution * **Given:** Number of children = 64. Sweets given to each = 7. Sweets leftover = 15. * First, calculate the total number of sweets successfully distributed to the children: $$\text{Distributed Sweets} = \text{Children} \times \text{Sweets per child}$$ $$\text{Distributed Sweets} = 64 \times 7$$ * Perform the multiplication: $64 \times 7 = 448$. * Next, add the leftover sweets to the distributed amount to find the initial total: $$\text{Total Sweets} = \text{Distributed} + \text{Leftover}$$ $$\text{Total Sweets} = 448 + 15 = 463$$ ### Exam Strategy & Shortcut Use the unit digit concept to save time. $64 \times 7 \rightarrow$ The unit digit is $4 \times 7 = 28 \rightarrow$ ends in 8. Add the remainder 15 $\rightarrow$ The unit digit is $8 + 5 = 13 \rightarrow$ ends in 3. Look at the options: only option (d) 463 ends in a 3. You can select it without doing the full calculation. ### Common Pitfall A simple calculation error during $64 \times 7$. Students sometimes forget to carry over correctly. Unit digit verification acts as a great safeguard against this. ### Final Answer Therefore, the correct answer is **463**.