Question

A can complete a work in 12 days and B can complete the same work in 18 days. If A and B work together for 4 days and then A leaves, how many more days will B take to finish the remaining work?

• A. 6 days
• B. 8 days
• C. 9 days
• D. 10 days

Hint:

Always try using the LCM method instead of adding fractions like $\frac{1}{12} + \frac{1}{18}$. Working with whole numbers keeps your scratch calculations faster and entirely avoids fractional errors!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Work-and-time problems can be simplified easily by finding the total capacity of the work. This capacity is determined by computing the Least Common Multiple (LCM) of the days given. From there, we compute the individual daily output (efficiencies) of each worker to track the total work completed stage by stage.

Step 2: Key Formula or Approach:
1. Total Work = $\text{LCM}(12, 18)$. 2. Efficiency = $\frac{\text{Total Work}}{\text{Total Days}}$. 3. $\text{Remaining Work} = \text{Total Work} - \text{Work done in first 4 days}$. 4. $\text{Days taken by B} = \frac{\text{Remaining Work}}{\text{Efficiency of B}}$.

Step 3: Detailed Explanation:
Let the total unit of work be the LCM of 12 and 18: \[ \text{Total Work} = 36 \text{ units} \] Now calculate the efficiency (work done per day) for both A and B: \[ \text{Efficiency of A} = \frac{36}{12} = 3 \text{ units/day} \] \[ \text{Efficiency of B} = \frac{36}{18} = 2 \text{ units/day} \] Combined efficiency of A and B working together: \[ \text{Combined Efficiency} = 3 + 2 = 5 \text{ units/day} \] They work together for 4 days, so the amount of work completed is: \[ \text{Work completed in 4 days} = 5 \text{ units/day} \times 4 \text{ days} = 20 \text{ units} \] Calculate the work left over after A exits: \[ \text{Remaining Work} = 36 - 20 = 16 \text{ units} \] Since A leaves, B must finish these 16 units alone. The number of extra days B needs is: \[ \text{Extra days for B} = \frac{\text{Remaining Work}}{\text{Efficiency of B}} = \frac{16}{2} = 8 \text{ days} \]

Step 4: Final Answer:
B will take 8 more days to finish the remaining work.