In a farm both men and women are working. Exactly one third of the staff bring one child each. One day each male employee planted 13 trees, each female employee planted 10 trees and each child planted 6 trees. A total of 159 trees were planted. How many women employees are there ?
Answers
Given : Exactly one third of the staff bring one child each
One day each male employee planted 13 trees,
each female employee planted 10 trees
and each child planted 6 trees.
A total of 159 trees were planted.
To Find : How many women employees are there
Solution:
Let say Men = M
and Women = W
Child = (M + W)/3
M + W must be divisible by 3
13M + 10W + 6(M + W)/3 = 159
=> 15M + 12W = 159
=> 5M + 4W = 53
=> M = 53 - 4W - 4M
=> M = 4(13 - W - M) + 1
=> M = 4K + 1
M = 1 , 5 , 9 , 13
Try each
5(1) + 4W = 53 => W = 12
1 + 12 = 13 is not Divisible by 3
5(5) + 4W = 53 => W = 7
5 + 7 = 12 Divisible by 3
M = 5 , W = 7 and Child = 4
M = 9
=> 5(9) + 4W = 53 => W = 2
9 + 2 = 11 is not Divisible by 3
Hence Total 7 Women employees are there
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