Question

A group of 20 girls plucked a total of 200 oranges. How many oranges can be plucked one of them?

(a) 24

(b) 10

(c) 32

(d) 7

I had been asked this question in class test.

My question is from Counting topic in portion Counting of Discrete Mathematics

Answer 1

Right answer is (a) 24

To elaborate: Suppose all of them plucked the different number of oranges. A girl can pluck at least 0 oranges and the number of oranges plucks by each student is distinct. So, total number of plucked oranges should be less than 100. But 0+1+2…..+19+20 = 210>200  a contradiction.

Thus there exist two girls who plucked the same number of oranges. If thus there exist two girls who plucked the same number of oranges. It means each girl of remaining 18 students plucked different number of oranges. Number of oranges Plucked by 18 students = 0+1+2+3…+17 = 153 oranges. Number of oranges plucked by remaining 2 student = 200 – 153 = 47.  Both students plucked same number of oranges. So, Number of oranges plucked by one of them = 47/2=24.