Question

On Arts day, 180 sweets were distributed equally among the students. Tasting one sweet Deepa said, “It is a pity that 9 of our friends are absent today.” Hearing this Deepu said, “Because of that we got one sweet more.”

a. Find out the total number of students,

b. How many students were present on that day?

Answer 1

a. Let the number of students = n

Number of sweets given to one student = \(\frac{180}{n}\)

Since 9 students were absent = \(\frac{180}{n-9}\)

∴ \(\frac{180}{n-9}=\frac{180}{n}+1\)

180n = 180(n - 9) + n(n - 9)

180n - 180n + 1620 - n² + 9n = 0

n² - 9n - 1620 = 0

\(n=\frac{9\pm \sqrt{81+4\times1620}}{2}\) = \(\frac{9\pm81}{2}\) or \(\frac{9-18}{2}\)

= 45 or -36

∴ Total number of students = 45

b. Total present = 45 – 9 = 36