Question

one baffallo gives 5 litre milk,one cow gives 2 litre milk and one goat gives 250 gram milk. then 20 animal gives 40 l milk how​

Answer 1

Let the number of buffalos, cows and goats be b,c and g respectively.

Since the total number of animals is 40

b+c+g=40 — (1)

The amount of milk given by 1 buffalo is 5 litres. Thus, the amount of milk given by b buffalos will be 5b litres.

Similarly,

amount of milk given by c cows will be 2c litres

amount of milk given by g goats will be 0.25g litres

Total amount of milk collected is given as 80 litres.

Thus,

5b + 2c + 0.25g = 80 — (2)

Multiplying (2) by 4 we get,

20b + 8c + g = 320 — (3)

Subtracting (1) from (3) we get,

19b + 7c = 280 — (4)

Now, b,c and g all have to be non negative integers as they represent the number of animals.

As we have been provided with only 2 equations having 3 unknowns, we have to do calculated guesswork at this stage, since we cannot use any other equation which could be solved with (4) simultaneously.

(4) can also be written as

(280–19b)/7 = c

=> (280/7) - (19b/7) = c

=> 40 - (19b/7) = c — (5)

For c be a non negative integer, there are only 2 possible values of b which are 0 and 7.

This is because c can only be an integer when (19b/7) is an integer. Thus b can only be a multiple of 7. The only values of b that satisfy this constraint and the equation (5) are 0 and 7.

Thus b=0 OR b=7

Putting these values of b we get 2 possible solutions,

When b=0, c=40, g=0

When b=7, c=21, g=12