World of Notebooks!

6 boys = 6 notebooks in 6 weeks

So 12 boys = 12 notebooks in 6 weeks

And 12 boys = 24 notebooks in 12 weeks.

4 girls = 4 notebooks in 4 weeks

So 12 girls = 12 notebooks in 4 weeks

And 12 girls = 36 notebooks in 12 weeks.

24 + 36 = 60 notebooks in total.

From the given data, one boy takes 6 weeks to complete a notebook and a girl takes 4 weeks to complete one notebook. So 12 girls and 12 boys will complete $12 \times 3 +12 \times 2 = 60 notebooks$ in 12 weeks.

Let number of boys, number of girls, number of weeks and number of notebooks

be B, G, W and N

N is proportional to B and W

Then, N is proportional to B W

Then

N = k B W, where k is a constant

From the data given we get

k = 1/6

Then

N = (1/6) B W ............... ( number of notebooks done by boys)............. (1)

similarly

N = (1/4) G W ............... ( number of notebooks done by girls) ............(2)

Since

B = G = W = 12

Then

Number of notebooks done by boys = 24

Number of notebooks done by girls = 36

The total number of notebooks done by boys and girls = 60

In order to solve this type of questions we need to find the man hours needed to accomplish certain work. In this case

4 girls x 4 weeks= Total manhours is ( 16 girl weeks) in order to write 4 notebooks so, time taken to write one notebook is 4/16= 1/4 ( notebooks per girl week) now there are 12 girls and 12 weeks. Hence, 1/4 x 12 x 12 = 36 notebooks

similarly for boys, answer comes out to be 24

hence total (24+ 36) = 60

If 6 boys can write 6 notebooks in 6 weeks, They can write 12 notebook in 12 weeks. And if they're 2 times more, they can write 24 books in 12 weeks.

If 4 girls can write 4 notebooks in 4 weeks, They can write 12 notebook in 12 weeks. And if they're 3 times more, they can write 36 books in 12 weeks.

24 + 36 = 60 books

6 boys = 6 books in 6 weeks
so 1 boy = 1/6 book in 1 week
we want to know for 12 boys in 12 weeks, so
(12 boys) (1/6 book) ( 12 weeks) = (12)(1/6)(12)= 24
Then:
4 girls = 4 books in 4 weeks
so 1 girl = 1/4 book in 1 weeks
(12girls)(1/4book)(12weeks) = 12(1/4)(12) = 36
24 + 36 = 60

6 boys complete 1 notebook per week. 4 girls complete 1 notebook per week.

Since you have "two packs" of 6 boys, and "three packs" of 4 girls, you'd get 2 boy-made notebooks and 3 girl-made notebooks per week, totalling 5 per week.

5 notebooks a week for 12 weeks gives you 5 X 12 = 60 notebooks.

In 6 weeks 6 boys can complete 6 notes,so in 1 week 1 boy can complete 6/(6 * 6)=1/6 notebooks,same way in 1 week 1 girl can complete (1/4) notebooks,so together in 1 week they can complete (1/6+1/4)=5/12,so In 12 weeks 12 boys and 12 girls can complete {(5/12) * 144}=60 notebooks.By the way wasn't this in Science Olympiad this year?

Since it takes 6 boys 6 weeks to complete 6 notebooks, it is understood that it would take 1 boy 6 weeks to complete 1 notebook.

In 12 weeks, 1 boy could complete 2 notebooks, so 12 boys would complete 24.

By the same reasoning, 1 girl could complete 3 notebooks in 12 weeks, so 12 girls would complete 36.

24 + 36 = 60

Set variables: b=boys ; g=girls ; n=notebooks ; w=weeks

We know that:

6b x 6w = 6n -------> b = $\frac{n}{6w}$

4g x 4w = 4n -------> g = $\frac{n}{4w}$

The question is: (12b + 12g) x 12w = (K)n

Substitute b and g: ( $\frac{2n}{w}$ + $\frac{3n}{w}$ ) x 12w = (K)n $\frac{5n}{w}$ x 12w = (K)n 60n = (K)n n = 60

I'll write here my solution, which is mainly based in logic. Apologies if it resembles some other user's solution (on purpose I didn't see anything).

As 6 boys are capable of writing 6 notebooks in 6 weeks, it is safe to say one alone completes one notebook in the same amount of time (6 weeks). Let's say we double the time to this boy, so he will have now 12 weeks. Then, if his work output is the same, he'll write 2 notebooks in 12 weeks (one the first 6, the other the last 6). Therefore, with 12 boys we expect to have $12 \times 2 = 24$ notebooks.

Then, the girls. 4 girls writing 4 notebooks in 4 weeks suggest one girl alone writes one notebook in 4 weeks. If we triple the time to this girl, ans assuming her work output will be the same, she will write 3 notebooks in 12 weeks (one per 4 weeks). Therefore, with 12 girls we expect to have $12 \times 3 = 36$ notebooks.

At the end, we will have $24 + 36 = 60$ notebooks in total.

Why did this work? Firstly, there is a linear relationship between the number of people and the notebooks written. We cannot mix the three variables because each guy is working in parallel with his/her duties during the same amount of time . Hence the need to know the work output of a person alone.

Secondly, we make the assumption the amount of work done by these people is always the same . With that in mind, we then extend the "deadline" for a person to see how many notebooks would he/she complete. This implies a linear relationship between the amount of time given and the work output.

Making sure the deadline is set the same for both genders, we can then safely integrate the number of girls and boys wanted, and, as each of them will be "in his/her own business", the total amount of notebooks will get first multiplied for each gender, and then added together.

What a nice problem to get your brain exercised! Thank you!

Boys: { 1 : 6 = X : 12 } where X = 2

Girls: { 1 : 4 = Y : 12 } where Y = 3

In total: 12(Y) + 12(X) = 36 + 24 = 60

6 boys, 6 notebooks in 6 weeks can be interpreted as 6 boys in 1 week produces 1 notebook. 12 boys, 12 weeks can be deduced as 12 boys in 1 week produces 2 notebooks, therefore in 12 weeks that's 24 notebooks

4 girls, 4 girls in 4 weeks can be interpreted as 4 girls in 1 week produces 1 notebook. 12 girls, 12 weeks can be deduced as 12 girls in 1 week produces 3 notebooks, therefore in 12 weeks that's 36 notebooks

36+24=60

Firstly, i saw that 12weeks, so when i look back in this question, found 4weeks and 6weeks

All weeks divided by 4,6.I got : girls have 3reps boys have 2reps and each rep girls allocated 4 ,boy's 6

So all girls /4 =3,all boys /6=2

So girl's work:3 $\times$ 3 $\times$ 4 = 36 Boy's work: 2 $\times$ 2 $\times$ 6= 24

Thought about it with the sets that were given. I have 2 sets of 6 boys, and I thought about how many notebooks one set of boys could finish in 12 weeks, then multiplied by 2 to get 24. Same with girls. One set of 4 girls could finish 12 notebooks in the alotted time, and multiplied by 3 is 36. 36 + 24 = 60.

Total amount of work done by 6 boys in 6 weeks = 6*6=36 Therefore work done by one boy in one week = 6/36 =1/6

Total amount of work done by 4 girls in 4 weeks =4*4=16 Therefore work done by one girl in one week= 4/16=1/4

Therefore work done by both (girls and boys) =1/6 12=2 boys In one week =1/4 12=3 girls =5

Therefore work done in 12 weeks =12*5=60 notebooks 💶💷💶💷💶💷💶💷💶💷💶💷💶💷💶💷💶💷💶💷💶💷💶💷💶💷💶💷💶💷💶💷💶💷💶💷💶💷💶😃😄😃😅😃😡😠😃😅😅😃😕😄😅😄😃😄😅😆😅😃😬😆😆😄😃😕😠😡😡😩😧😦😕😠😧😨😬😕👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👏👐👐👏👏👏👏📗📘📙📚📚📔📒📑📓📕📒📒📙📘📗📘📙📚📔📒📑📓📕📕📓📑📒📔📙📙📘📗📗📘📙📚📔📒📑

1 boy one notebook 6 weeks so 12 boys 12 notebooks in 6 weeks so 12 boys 24 notebooks in twelve weeks similarly 12 girls 36 notebooks in 12 weeks finally 24+36=60

6 boys = 6 notebooks in 6 weeks. So 6 boys = 1 notebook in 1 week. Therefore 1 boy can complete 1/6 of a notebook in 1 week. Following the same logic for girls give you 1 girl can complete 1/4 of a notebook in one week. In 12 weeks, one girl can complete (1/4)(12), or 3 notebooks. Multiply that by 12 girls and you get 36 notebooks for the girls. For the boys: (1/6)(12)(12) = 24 Add this up and you get 60 :)