In a class of MBA students `16.66%` students are from Science background and `12.5%` students are from commerce background and `66.6%` students from arts background and rest are from Engineering background. The minimum possible students of engineering background are :

Options

A. `88`
B. `99`
C. `77`
D. `66`

Answer

To solve the problem step by step, we need to determine the minimum possible number of students from the Engineering background in a class of MBA students. We will start by analyzing the percentages given for each background.

### Step 1: Understand the Percentages
The percentages of students from different backgrounds are:
- Science: 16.66%
- Commerce: 12.5%
- Arts: 66.66%
- Engineering: Remaining percentage

### Step 2: Convert Percentages to Fractions
To make calculations easier, we can convert the percentages into fractions:
- 16.66% = 1/6 (approximately)
- 12.5% = 1/8
- 66.66% = 2/3 (approximately)

### Step 3: Find the Least Common Multiple (LCM)
To find the total number of students, we need to find the least common multiple (LCM) of the denominators of the fractions:
- The denominators are 6, 8, and 3.
- The LCM of 6, 8, and 3 is 24.

### Step 4: Calculate the Number of Students from Each Background
Now, we can calculate the number of students from each background based on the total number of students being 24:
- Science: (1/6) of 24 = 4 students
- Commerce: (1/8) of 24 = 3 students
- Arts: (2/3) of 24 = 16 students

### Step 5: Calculate Total Students from Known Backgrounds
Now, we add the number of students from Science, Commerce, and Arts:
- Total from known backgrounds = 4 (Science) + 3 (Commerce) + 16 (Arts) = 23 students

### Step 6: Determine Students from Engineering Background
To find the students from the Engineering background, we subtract the total known students from the total class size:
- Total students in the class = 24
- Students from Engineering = 24 - 23 = 1 student

### Conclusion
The minimum possible number of students from the Engineering background is **1 student**.

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