Question

In a randomly arranged order of a field there are some dogs and ducks. When the heads are counted they are found to be 360 while the legs are counted to be 900. Find the number of dogs in the field.

1. 95
2. 90
3. 81
4. 75

Answer 1

Correct Answer - Option 2 : 90

Given:

Number of total Heads = 360

Number of total Legs = 900

Concept used:

As both dogs and ducks have one head.

Dogs have 4 legs and ducks have 2 legs.

Calculation:

No. of heads = number of duck + number of dogs

⇒ No. of legs = 2 × number of ducks + 4 × number of dogs

Let the number of ducks and dogs be X and Y respectively.

⇒ X + Y = 360      ------(1)

⇒ 2X + 4Y = 900      ------(2)

Multiply by eq. (1) with 2 

⇒ 2(X + Y) = 360 × 2 

⇒ 2X + 2Y = 720      ------(3)

Subtract eq. (3) from eq. (2)

⇒ 2X + 4Y – (2X + 2Y) = 900 – 720 

⇒ 2X + 4Y – 2X – 2Y = 180 

⇒ 2Y = 180 

⇒ Y = 90  

⇒ Number of dogs = 90

∴ The number of dogs is 90.