Kamal has 160 toffees. He gave 5% toffees to Ravi, 15% toffees to Anita and one-fourth of the toffees to Gagan. How many toffees are left with Kamal after the distribution?

### Concept & Logic This problem is solved efficiently by tracking percentages instead of calculating individual quantities. Converting fractions to percentages unifies the data. $$ \text{Remaining \%} = 100\% - (\text{Sum of distributed percentages}) $$ ### Step-by-Step Solution * **Given**: * Total toffees = 160 * To Ravi = $5\%$ * To Anita = $15\%$ * To Gagan = $\frac{1}{4}$ of total * **Deduction**: * Convert Gagan's share to a percentage: $\frac{1}{4} = 25\%$. * Total percentage distributed = $5\% + 15\% + 25\% = 45\%$. * Percentage of toffees left = $100\% - 45\% = 55\%$. * **Calculation**: * Number of toffees left = $55\%$ of 160. * Calculation: $\left( \frac{55}{100} \right) \times 160 = 55 \times 1.6 = 88$. ### Exam Strategy & Shortcut Always unify units (fractions to percentages). Total given away is $5 + 15 + 25 = 45\%$. Left over is $55\%$. Mentally split the remaining percentage for faster calculation: $50\%$ of 160 is 80. $5\%$ of 160 is 8. $80 + 8 = 88$. Done mentally in 10 seconds. ### Common Pitfall A common mistake is calculating the absolute number of toffees for each person sequentially ($5\%$ of 160, then $15\%$ of 160, then $\frac{1}{4}$ of 160) and then subtracting the sum from 160. This introduces multiple calculation steps and heavily increases the risk of arithmetic errors. ### Final Answer **Therefore, the correct answer is 88.**