In a seminar, 5 teachers and 7 students spent money on books. The average spending of all of them together was ₹260. The average spending of the teachers alone was ₹400. Find the average spending amount of the students.

The correct option is ₹160.

Let us find the average spending amount of the students step-by-step.

Step 1: Understand the given data
Number of teachers = 5
Number of students = 7
Total number of people in the seminar = 5 + 7 = 12
Average spending of all 12 people = ₹260
Average spending of the 5 teachers alone = ₹400

Step 2: Calculate the total spending of all 12 people
The formula for average is:
Average = Total Spending / Number of People
Therefore, Total Spending = Average × Number of People
Total spending of all 12 people = 12 × ₹260
Total spending of all 12 people = ₹3,120

Step 3: Calculate the total spending of the teachers
Total spending of the 5 teachers = 5 × ₹400
Total spending of the 5 teachers = ₹2,000

Step 4: Find the total spending of the students
Total spending of the 7 students = Total spending of everyone - Total spending of the teachers
Total spending of the 7 students = ₹3,120 - ₹2,000
Total spending of the 7 students = ₹1,120

Step 5: Calculate the average spending of the students
Average spending of the students = Total spending of students / Number of students
Average spending of the students = ₹1,120 / 7
Average spending of the students = ₹160

Thus, the average spending amount of the students is ₹160.