A can do a piece of work in 48 days. If B is 50% more efficient than A, then in how many days can B do the same work?

Options

A. 24
B. 32
C. 18
D. 15

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Determine A's work rate
A can complete the work in 48 days. Therefore, A's work rate (amount of work done in one day) is:
\[ \text{Work rate of A} = \frac{1 \text{ work}}{48 \text{ days}} = \frac{1}{48} \text{ work per day} \]

**Hint:** To find the work rate, divide the total work (1 unit) by the number of days taken to complete it.

### Step 2: Calculate B's efficiency
B is 50% more efficient than A. This means B's efficiency is:
\[ \text{Efficiency of B} = \text{Efficiency of A} + 50\% \text{ of Efficiency of A} = \frac{1}{48} + \frac{1}{2} \times \frac{1}{48} \]
Calculating 50% of A's efficiency:
\[ \frac{1}{2} \times \frac{1}{48} = \frac{1}{96} \]
Now add this to A's efficiency:
\[ \text{Efficiency of B} = \frac{1}{48} + \frac{1}{96} \]

**Hint:** To add fractions, find a common denominator.

### Step 3: Find a common denominator
The least common multiple of 48 and 96 is 96. Convert A's efficiency:
\[ \frac{1}{48} = \frac{2}{96} \]
Now we can add:
\[ \text{Efficiency of B} = \frac{2}{96} + \frac{1}{96} = \frac{3}{96} = \frac{1}{32} \]

**Hint:** When adding fractions, convert them to have the same denominator.

### Step 4: Calculate the number of days B takes to complete the work
If B's work rate is \(\frac{1}{32}\) work per day, then the number of days B takes to complete the entire work is the reciprocal of B's work rate:
\[ \text{Days taken by B} = \frac{1}{\frac{1}{32}} = 32 \text{ days} \]

**Hint:** To find the total time taken to complete the work, take the reciprocal of the work rate.

### Final Answer
B can complete the work in **32 days**.