In a farm there are cows and hens. If heads are counted there are 180, if legs are counted there are 420. The number of cows in the farm is -

Question: In a farm there are cows and hens. If heads are counted there are 180, if legs are counted there are 420. The number of cows in the farm is -

Solution:
Let, the number of cows be x.
Then, number of hens would be (180 - x)

ATQ,
(180 - x) × 2 + 4x = 420
⇒ 360 - 2x + 4x = 420
⇒ 2x = 420 - 360
⇒ 2x = 60
⇒ x = 60/2
∴ x = 30

∴ The number of cows 30.