Question

100 people 100 fruits. distribution 1male get 4 fruits, 1 female get 2 fruits,4 children get 1 fruit. find male,female,children number?

Answer 1

Given:

100 people 100 fruits.

1 male get 4 fruits, 1 female get 2 fruits,4 children get 1 fruit.

To Find :

Number of male , female and Children,

Solution:

Let number of males = M

number of females = F

number of children = C

• Then M + F + C = 100 .

Also

• Total fruits = 4M + 2F + 0.25C = 100

Since all number are whole numbers , 0.25C should be a whole number as well.

Then C should be a multiple of 4.

But Since coefficients of M and C are multiples of 2 , 0.25C should be an even number.

Therefore C is a multiple of 8 .

• C can be 8 , 16 , 24 , 32 , 40 , 48 , 56 , 64 , 72 , 80 , 88 , 96.

Let C = 48

• Then M + F = 100 - 48 = 52 .
• 4M + 2F = 100 - 12 = 88
• 2M + F = 44
• M  = -8 , which is not possible.

Therefore C should be a bigger value.

Lets consider the mid value of in the remaining bigger sequence.

Let C = 72.

• M + F = 28
• 2M  + F = 100 - 18 = 82
• M = 54
• Then F = -26 is negative , not possible.
• Therefore we can consider a value of C between 48 and 72.

Let C = 56

• M + F = 44
• 2M + F  = 100 - 14 = 86
• F =  2.

• M = 42

This is the correct answer.

Number of males is 42, number of females is 2 and number of children is 56.