A can do a certain job in 12 days. B in 60% more efficient than A. What is the number of days it takes B to do the same piece of work ?

Answer

To solve the problem step by step, we will start by determining the work done by A and then find out how much work B can do based on his efficiency.

### Step 1: Determine A's work rate
A can complete the job in 12 days. Therefore, A's work rate per day is:
\[ \text{Work rate of A} = \frac{1}{12} \text{ (job per day)} \]

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

### Step 2: Calculate B's efficiency
B is 60% more efficient than A. To find B's efficiency, we first need to calculate what 60% of A's work rate is:
\[ \text{60% of A's work rate} = 0.6 \times \frac{1}{12} = \frac{0.6}{12} = \frac{0.6}{12} = \frac{6}{120} = \frac{1}{20} \]
Now, we add this to A's work rate to find B's work rate:
\[ \text{Work rate of B} = \text{Work rate of A} + \text{60% of A's work rate} = \frac{1}{12} + \frac{1}{20} \]

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

### Step 3: Find a common denominator
The least common multiple (LCM) of 12 and 20 is 60. We will convert both fractions to have a denominator of 60:
\[ \frac{1}{12} = \frac{5}{60} \quad \text{and} \quad \frac{1}{20} = \frac{3}{60} \]
Now we can add them:
\[ \text{Work rate of B} = \frac{5}{60} + \frac{3}{60} = \frac{8}{60} = \frac{2}{15} \]

**Hint:** When adding fractions, ensure both fractions are expressed with the same denominator.

### Step 4: Calculate the number of days B takes to complete the work
Now that we know B's work rate is \(\frac{2}{15}\) (jobs per day), we can find the number of days B takes to complete the job:
\[ \text{Days taken by B} = \frac{1 \text{ job}}{\text{Work rate of B}} = \frac{1}{\frac{2}{15}} = \frac{15}{2} = 7.5 \text{ days} \]

**Hint:** To find the number of days, divide 1 by the work rate.

### Final Answer
B takes **7.5 days** to complete the same piece of work.