A is twice as good a workman as B. If they work together, they can complete a job in 18 days. If A alone does the job, in how many days he will complete the job?

### Concept & Strategy "Twice as good a workman" means twice the efficiency. By setting up an efficiency ratio, you can easily calculate the total units of work and divide it by an individual's efficiency. $$ \text{Total Work} = \text{Combined Efficiency} \times \text{Combined Time} $$ ### Step-by-Step Solution 1. **Establish the efficiency ratio:** Let B's efficiency (work units per day) be 1. Since A is twice as good, A's efficiency is 2. 2. **Calculate combined efficiency:** Combined efficiency (A + B) = $2 + 1 = 3$ units per day. 3. **Determine the total work:** They complete the job together in 18 days. Total Work = Combined Efficiency $\times$ Time Total Work = $3 \times 18 = 54$ units. 4. **Calculate time for A alone:** Time taken by A = $\frac{\text{Total Work}}{\text{A's Efficiency}}$ Time taken by A = $\frac{54}{2} = 27$ days. ### Exam Strategy & Shortcut Using ratios is the fastest method here. Speed ratio A : B = 2 : 1. Therefore, Time ratio A : B = 1 : 2. Let A's time = $x$, B's time = $2x$. Combined formula: $\frac{x \cdot 2x}{x + 2x} = 18$ $\frac{2x^2}{3x} = 18 \implies \frac{2x}{3} = 18 \implies 2x = 54 \implies x = 27$. A takes 27 days. ### Common Pitfall A common mistake is misinterpreting the phrasing and applying the ratio incorrectly to time instead of efficiency, which would lead to calculating 54 days for A instead of B. ### Final Answer Therefore, the correct answer is **27 days**.