Question

A and B together can complete a piece of work in 12 days. A alone can complete it in 20 days. In how many days can B alone complete the work?

• A. 24 days
• B. 28 days
• C. 30 days
• D. 36 days

Hint:

Try the Total Work (LCM) method to avoid fractions! Take the LCM of 12 and 20, which is 60 units (total work). Combined efficiency of A + B = $\frac{60}{12} = 5$ units/day. Efficiency of A alone = $\frac{60}{20} = 3$ units/day. Efficiency of B = $5 - 3 = 2$ units/day. Days taken by B = $\frac{60 \text{ total units}}{2 \text{ units/day}} = 30$ days!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Time and work problems can be solved by calculating the rate of work done per day (one-day work efficiency). The total work is considered as 1 whole unit. If two people work together, their combined daily efficiency is the sum of their individual daily efficiencies.

Step 2: Key Formula or Approach:
1. $\text{One day's work} = \frac{1}{\text{Total number of days taken}}$ 2. $\text{Efficiency of B} = \text{Combined efficiency of (A + B)} - \text{Efficiency of A}$

Step 3: Detailed Explanation:
Let's find the daily work rates from the given information: Work rate of A and B together ($A + B$) = $\frac{1}{12}$ of the work per day. Work rate of A alone = $\frac{1}{20}$ of the work per day. Now, subtract A's daily rate from the combined rate to find B's individual daily rate: \[ \text{Work rate of B alone} = \frac{1}{12} - \frac{1}{20} \] Find a common denominator for 12 and 20, which is 60: \[ \text{Work rate of B alone} = \frac{5}{60} - \frac{3}{60} = \frac{2}{60} = \frac{1}{30} \] Since B can complete $\frac{1}{30}$ of the total work in one single day, the total time required for B to finish the entire project alone is the reciprocal of this rate: \[ \text{Total days taken by B} = \frac{1}{\frac{1}{30}} = 30 \text{ days} \]

Step 4: Final Answer:
B alone can complete the work in 30 days.