A can do a piece of work in 24 days. If B is 50% more efficient than A, then in how many days can B do the same work?

Options

A. 12
B. 16
C. 18
D. 15

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine A's work rate
A can complete the work in 24 days. Therefore, A's work rate is:
\[ \text{Work rate of A} = \frac{1 \text{ work}}{24 \text{ days}} = \frac{1}{24} \text{ work per day} \]

### Step 2: Calculate B's efficiency
B is 50% more efficient than A. To find B's work rate, we first calculate 50% of A's efficiency:
\[ \text{50% of A's work rate} = 0.5 \times \frac{1}{24} = \frac{1}{48} \]
Now, we add this to A's work rate to find B's work rate:
\[ \text{Work rate of B} = \text{Work rate of A} + \text{50% of A's work rate} = \frac{1}{24} + \frac{1}{48} \]

### Step 3: Find a common denominator
To add the fractions, we need a common denominator. The least common multiple of 24 and 48 is 48. We convert \(\frac{1}{24}\) to have a denominator of 48:
\[ \frac{1}{24} = \frac{2}{48} \]
Now we can add the two fractions:
\[ \text{Work rate of B} = \frac{2}{48} + \frac{1}{48} = \frac{3}{48} = \frac{1}{16} \text{ work per day} \]

### Step 4: Calculate the time taken by B to complete the work
To find out how many days B takes to complete the work, we take the reciprocal of B's work rate:
\[ \text{Days taken by B} = \frac{1 \text{ work}}{\text{Work rate of B}} = \frac{1}{\frac{1}{16}} = 16 \text{ days} \]

### Final Answer
B can complete the work in **16 days**.

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