Maganlal, a worker, makes an article in every `( 2)/( 3) `h. If he works for `7 ( 1)/( 2)`h, then how many articles will he make ?

Options

A. `11(1)/( 4)`
B. `11(1)/( 3)`
C. `11(1)/( 6)`
D. `11(2)/( 5)`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the problem
Maganlal makes one article in \( \frac{2}{3} \) hours. We need to find out how many articles he can make in \( 7 \frac{1}{2} \) hours.

### Step 2: Convert mixed number to improper fraction
Convert \( 7 \frac{1}{2} \) hours into an improper fraction:
\[ 7 \frac{1}{2} = 7 + \frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2} \text{ hours} \]

### Step 3: Set up the relationship
If Maganlal makes 1 article in \( \frac{2}{3} \) hours, we can set up the equation to find the number of articles \( x \) he can make in \( \frac{15}{2} \) hours:
\[ x \times \frac{2}{3} = \frac{15}{2} \]

### Step 4: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{15}{2} \div \frac{2}{3} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ x = \frac{15}{2} \times \frac{3}{2} \]

### Step 5: Multiply the fractions
Now, multiply the fractions:
\[ x = \frac{15 \times 3}{2 \times 2} = \frac{45}{4} \]

### Step 6: Convert to mixed number
Convert \( \frac{45}{4} \) into a mixed number:
\[ 45 \div 4 = 11 \text{ R } 1 \Rightarrow 11 \frac{1}{4} \]

### Conclusion
Maganlal can make \( 11 \frac{1}{4} \) articles in \( 7 \frac{1}{2} \) hours.

---