Let's write a story and work out the problem finding relation (direct/inverse) between them.

(a) First let’s write story for the following data:

Problem: In a district there are 24 villages having same number of people in each village. These villages consume the whole food stock in 12 days. Now in another district there are 36 villages with same number of people in it, consume the same amount of food stock, then calculate using proportion the number of days the food stock will last?

Given: 24 villages consume whole food stock in 12 days.

To find how many days will the food stock last if 36 villages consume the same amount of food stock.

Solution: Here we need to apply inverse proportion as the number of villages increases, the time taken to finish the stock must decrease,

24villages consume whole food stock in 12 days

⇒ total amount of food stock =24× 12………(i)

Another distric has 36 villages consuming the same amount of food stock. Let the number of days the food stock last = x, then

⇒ total amount of food stock = 36×(x)………(ii)

Now in both cases the food stock quantity is equal, hence proportion (i) and proportion (ii) should be equal, so we get the following relation,

⇒ 24× 12=36×(x)

⇒

So, Number of days the food stock last in another district having 36 villages = 8 days

(b) Now let’s write the problem for second set of data:

Problem: There was a co-operative society, 30 members from this society took 5 hours to clean the society on first day. The next day 5 member of the society resigned, then on that day how many hours it will take to clean the society?

Given: 30 members of the co-operative society cleaned the society in 5 hours.

To find how many hours it will take to clean the society the next day when 5 members resigned.

Solution: Here we need to apply inverse proportion as the number of members decreases, the time taken to finish the cleaning must increase,

30 members cleaned the society in 5hours.

⇒ total amount of work done =30×5………(i)

5 members resigned the next day, so the number of members left = 30-5=25. Let the number of hours required to clean the society = x, then

⇒ total amount of work done = 25×(x)………(ii)

Now in both cases the amount of work done in cleaning the society is same, hence proportion (i) and proportion (ii) should be equal, so we get the following relation,

⇒ 30×5=25×(x)

⇒

So, Number of hours to clean the society when 5 members resigned = 6 days