Question

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

• A. 25 days
• B. 30 days
• C. 40 days
• D. 50 days

Hint:

In work problems: \[ \text{Combined efficiency} = \text{Sum of individual efficiencies} \]

Answer 1

The Correct Option is B

Concept: Work problems are solved using efficiency or work rates. If a person completes work in \(n\) days, then: \[ \text{One day's work} = \frac{1}{n} \] Combined work rates are added together.

Step 1: Find the work rate of A and B together.
A and B together complete work in 12 days. Thus: \[ (A+B)'s \text{ one day's work} = \frac{1}{12} \]

Step 2: Find A's individual work rate.
A alone completes work in 20 days. Therefore: \[ A's \text{ one day's work} = \frac{1}{20} \]

Step 3: Calculate B's work rate.
\[ B's \text{ work rate} = \frac{1}{12} - \frac{1}{20} \] Taking LCM: \[ = \frac{5-3}{60} \] \[ = \frac{2}{60} \] \[ = \frac{1}{30} \]

Step 4: Determine time taken by B alone.
If B completes: \[ \frac{1}{30} \] of work in one day, then B alone completes full work in: \[ 30 \text{ days} \]

Step 5: Write the final conclusion.
Hence, B alone can complete the work in: \[ \boxed{30 \text{ days}} \]