There are 4 types of animals in a farm. Cows, Goats, Sheep and Buffalos. A cow gives 8 liters of Milk everyday. A Buffalo gives 4 liter of milk everyday. Goat gives a liter of milk everyday and Sheep gives a forth of a liter of milk everyday. If there are 100 animals in farm and gives 100 liter of milk everyday. Find the total no. of each animals.
Answers
Answer:
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
Step-by-step explanation:
hopes its helps you...
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
Step-by-step explanation:
hopes its helps you...