Question

In a group of buffaloes and ducks the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group ?

Answer 1

Let the Number of Buffaloes in the Group be : B

Let the Number of Ducks in the Group be : D

We know that : A Buffalo has 4 Legs and A Duck has 2 Legs

⇒ Number of Legs of Buffaloes in the Group : 4 × B

⇒ Number of Legs of Ducks in the Group : 2 × D

⇒ Total Number of Legs in the Group = (4 × B) + (2 × D)

We know that : A Buffalo and A Duck , Both have One Head

⇒ Number of Heads of Buffaloes in the Group : B

⇒ Number of Heads of Ducks in the Group : D

⇒ Total Number of Heads in the Group = (B + D)

Given : The Number of Legs are 24 More than Twice the Number of Heads

⇒ (4 × B) + (2 × D) - 24 = 2(B + D)

⇒ 4B + 2D - 24 = 2B + 2D

⇒ 2B - 24 = 0

⇒ 2B = 24

⇒ B = 12

⇒ Number of Buffaloes in the Group are : 12

Answer 2

Explanation:

Let the number of buffaloes be x and the number of ducks be y.

=> 4x + 2y = 2 (x + y) + 24

=> 2x = 24 => x = 12