A does 20% less work than B. If A can complete a piece of work in $7 \frac{1}{2}$ hours, then B can do it in

### Concept & Percentage Efficiency "20% less work" means the efficiency is 20% lower. Setting the standard worker's rate to 100 or 100% simplifies the derivation of the ratio. ### Step-by-Step Solution 1. **Establish the Efficiency Ratio:** Let B's efficiency be 100 units/hour. A does 20% less work, so A's efficiency is $100 - 20 = 80$ units/hour. Efficiency ratio of A : B = 80 : 100 = 4 : 5. 2. **Calculate Total Work:** A takes $7 \frac{1}{2}$ hours to complete the work. Convert to an improper fraction: $\frac{15}{2}$ hours. Total Work = A's Efficiency $\times$ A's Time Total Work = $4 \times \frac{15}{2} = 2 \times 15 = 30$ units. 3. **Calculate B's Time:** Time = $\frac{\text{Total Work}}{\text{B's Efficiency}}$ Time for B = $\frac{30}{5} = 6$ hours. ### Exam Strategy & Shortcut Use inverse ratios. Since efficiency ratio A : B = 4 : 5, the time ratio A : B = 5 : 4. This means B takes $\frac{4}{5}$ of the time A takes. Time for B = $\frac{4}{5} \times \frac{15}{2} = \frac{60}{10} = 6$ hours. ### Common Pitfall A common mistake is assuming that because A takes 20% less work, B will simply take 20% less time than A, which mathematically misinterprets the inverse relationship between speed and time. ### Final Answer Therefore, the correct answer is **6 hours**.