A farm rears geese and dogs. The headcount in the farm is 84 and the leg count is 282. How many geese are there? *
Answers
Answer:
Let’s make it simple,
Let’s assume there are equal dogs and geese.
As there are 84 dogs and geese, and we are assuming they are equal in proportion,there are 42 dogs and 42 geese.
Each dog has 4 legs = 42*4 = 168
Each goose has 2 legs = 42*2 = 84
Leg count obtained is = 168 + 84 = 252
But the given leg count is 282.
Therefore to match with the given leg count, we have to increase the count of the animal having more legs i.e dogs.
For every increase in a dog, no,of legs increased are 4, in the same way one goose will be decreased,no.of legs lost are 2.
Therefore for every single exchange,no.of legs increased are = 4–2 = 2
No.of legs to be increased = 282–252 = 30
No.of animals to be exchanged = 30/2 = 15
No.of dogs = 42 + 15 = 57
No.of geese = 42–15 = 27