Study the given pie-chart and answer the question that follows.

The pie-chart represents the total number of valid votes obtained by four students who contested for school leadership. The total number of valid votes polled was 720.

What is the minimum number of votes obtained by any candidate?

The correct answer is 120.

From the given pie-chart, we can see the central angles representing the votes obtained by the four candidates:

1. Yasin = 60°
2. Paramjit Kaur = 80°
3. Vishwanath = 100°
4. Siva Raman = 120°

The total number of valid votes polled is 720, which corresponds to the total angle of a circle, i.e., 360°.

To find the minimum number of votes obtained by any candidate, we identify the candidate with the smallest central angle. Here, Yasin has the minimum central angle of 60°.

We can calculate the minimum number of votes as follows:

$\text{Minimum votes}=\left(\frac{\text{Minimum Central Angle}}{360°}\right)\times \text{Total Votes}$

$\text{Minimum votes}=\left(\frac{60}{360}\right)\times 720$

$\text{Minimum votes}=\frac{1}{6}\times 720=120$

Thus, the minimum number of votes obtained by any candidate is 120.