Let the total number of students be n. For each pair, two cards are sent and the total number of pairs can be nC2 So, total cards = 2 x nC2 or 2 x nC2 = 1980,= 2 x n(n-1)/21 = 1980∴ n² - n = 1980or n² - 45n + 44n - 1980 = 0or n(n - 45) + 44(n - 45) = 0or (n + 44) (x - 45) = 0∴ n = 45, - 44 (Now, discard - value)∴ n = 45
Let the numbers be x, x + 2, x + 4, x + 6, and x + 8Avg = x + x + 2 + x + 4 + x + 6 + x + 8/5 = 40Therefore, 5x + 20 = 200Therefore, x = 180/5 = 36Therefore, r = x + 4 = 40 s = x + 6 = 42Therefore, Product = 1680
EXAMIANS