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 Question:
This is a "Time and Work" problem involving two individuals with different rates of efficiency. The scenario describes a two-stage process: first, both individuals work together, and then one individual completes the remaining task alone. To solve this, we must determine the total volume of work and the daily output (efficiency) of each person. By tracking how much work is completed during the initial phase, we can calculate what remains and how much time the second person needs to finish it based on their specific speed.
Step 2 : Key Formulas and approach:
The most efficient approach is the LCM method:
Total Work = $\text{LCM of time taken by individuals}$.

Efficiency = $\frac{\text{Total Work}}{\text{Days taken}}$.

Work Done = $\text{Efficiency} \times \text{Time}$.

Remaining Work = $\text{Total Work} - \text{Work Done}$.

Step 3 : Detailed Explanation:

Step 1: Find the total units of work. $\text{LCM}(12, 18) = 36$ units.

Step 2: Calculate daily efficiency. Efficiency of A = $36 \div 12 = 3$ units/day. Efficiency of B = $36 \div 18 = 2$ units/day.

Step 3: Find their combined daily efficiency. Total efficiency = $3 + 2 = 5$ units/day.

Step 4: Calculate work done in the first 4 days while they work together. Work = $5 \times 4 = 20$ units.

Step 5: Calculate the remaining work. Remaining work = $36 - 20 = 16$ units.

Step 6: Determine how long B takes to finish these 16 units. Time for B = $\frac{\text{Remaining work}}{\text{Efficiency of B}} = \frac{16}{2} = 8$ days.

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