The average weight of some students in a section is 35.5 kg. Twelve of them whose average weight is 37 kg leave the section and another 5 students with weights 40 kg, 39.5 kg, 38.5 kg, 42 kg and 47.5 kg join the section, and thereby the average weight of the students in the section increases by 300 g. The number of students, initially, in the section, was:

Correct option is A

Given:
The average weight of some students = 35.5 kg
12 students leave the section
→ Their average weight = 37 kg
5 new students join
→ Their weights = 40 kg, 39.5 kg, 38.5 kg, 42 kg, 47.5 kg
After this change, the new average weight increases by 300 g
→ So, new average = 35.5 + 0.3 = 35.8 kg
We are to find the initial number of students in the section

Formula Used:

1. Total weight = Average × Number of students
2. New total weight = Initial total weight − Weight of students who left + Weight of students who joined
3. Use algebraic equation to form and solve:
• Let initial number of students = x

Solution:

Step 1: Let the initial number of students be x

• Average weight = 35.5 kg
• So, total initial weight = 35.5 × x

Step 2: 12 students leave

• Their average = 37 kg
• So, total weight they carried away = 12 × 37 = 444 kg

Step 3: 5 new students join

• Their weights = 40 + 39.5 + 38.5 + 42 + 47.5 = 207.5 kg

Step 4: New number of students

• = x − 12 + 5 = x − 7
• New average weight = 35.5 + 0.3 = 35.8 kg
• So, new total weight = 35.8 × (x − 7)

Step 5: Form the equation

New total weight = Old total weight − Weight of 12 students + Weight of new 5 students

So,

35.8 × (x − 7) = 35.5 × x − 444 + 207.5
35.8x − 250.6 = 35.5x − 236.5

Now,

0.3x = 14.1
x = 14.1 / 0.3 = 47

Final Answer: 47