A group of students decided to buy a watch priced between 170 and 195 rupees.…

When a fixed total cost is split equally among a group, each person's share equals the total cost divided by the number of people. If the group size decreases while the total cost stays the same, each person's share increases — and the size of that increase links the original group size, the new group size, and the total cost through a simple equation.

1. Let the price of the watch be Rs. x and the original number of students be n. Each student's planned share is x/n.

2. After 2 students back out, (n − 2) students remain, and each now pays x/(n − 2).

3. The new share exceeds the planned share by Re. 1, so x/(n − 2) − x/n = 1.

4. Combine the fractions: x·[n − (n − 2)] / [n(n − 2)] = 1, which simplifies to x = n(n − 2)/2.

5. Apply the price range: since the watch costs between Rs. 170 and Rs. 195, substitute x = n(n − 2)/2 into 170 ≤ x ≤ 195, giving 340 ≤ n2 − 2n ≤ 390.

6. Solving n2 − 2n − 340 = 0 gives n ≈ 19.4, and solving n2 − 2n − 390 = 0 gives n ≈ 20.7. Since n must be a whole number lying between these two bounds, n = 20.

7. Substitute n = 20 back into x = n(n − 2)/2: x = 20 × 18 / 2 = 180.

Check: with 20 students, each was to pay 180/20 = Rs. 9. With 2 fewer students (18 remain), each pays 180/18 = Rs. 10 — exactly Re. 1 more, matching the condition. So the price of the watch is Rs. 180.