Question

There are 100 mangoes in a basket, the population is 100, one man gives four fruits, one woman two fruits, four children one fruit, but how many men, women and children?​

Answer 1

Given :

Total number of mangoes = 100

Total population = 100

Number of fruit given to each men = 4

Number of fruit given to each women = 2

Number of fruit given to each children = $\dfrac{1}{4}$

To Find :

Number of men

Number of women

Number of children

Solution :

∵ Total population = 100

i.e number of men + number of women + number of children = 100

i.e  m + w + c = 100           ..........1

∵  Total mangoes = 100

So,  Total mangoes = number of mangoes given to each men × number of men +  number of mangoes given to each women × number of women +  number of mangoes given to each children × number of children

i.e  4 m + 2 w + $\dfrac{1}{4}$  c = 100        ..........2

From eq 1 and 2

  6 men = 6 × 4 = 24 mangoes

  30 women = 30 × 2 = 60 mangoes

  64 children = $\dfrac{64}{4}$ = 16 mangoes

So, The number of population = 6 men + 30 women + 64 children = 100

And Total number of mangoes = 24 + 60 + 16 = 100

Hence, The number of men is 6

            The number of women is 30

            The number of children is 64  

Answer

Answer 2

Given data:

• According to the given question, there are 100 mangoes in a basket.
• The population is 100 people.
• However, one gave four fruits to a man, two fruits to a woman, and one fruit to four children.

To find:

How many men, women, and children were there?

Solution:

For a while, the total number of men who took the fruits be 'x' and the number of females be 'y'.

Then, the number of children becomes 100 - (x + y).

The equation that comes when these are arranged in the order given is:

4x + 2y + [(100 - (x + y)) / 4] = 100

16x + 8y + 100 - x - y = 100 * 4

15x + 7y = 400 - 100

15x + 7y = 300

The rephrased equation will be

x = (300 - 7y) / 15

Since there are two unknown variables ​​here, we need to see which values ​​should be placed in the 'y' position, such that the equation is completely divided and gives a natural number as an output.

The resulting x,y pairs are: [without 0]

If y = 15 then x = 13.

If y = 30 then x = 6.

On substitution, the possible answers that we found here are:

Answer 1:

Number of females: 15

Number of males: 13

Number of children: 72

Or

Answer 2:

Number of females: 30

Number of males: 6

Number of children: 64

Learn more:

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2. There are 100 mangoes in a gampa, the population is 100, one man gives four teeth, one woman two teeth, four children one fruit, but how many men, women, and children?

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