Mixtures Question: Pigeons & Horses

This aptitude practice question is a mixtures and alligation question. Concept tested: The question can be solved using a simple linear equation or by setting up alligation.

Question

A farmer counted the heads of the animals / birds in the farm and found it to be 80. When he counted the legs he found it to be 260. If the farm had either pigeons or horses and nothing else, how many horses were there in the farm? In the farm, each horse had four legs and each pigeon had two legs.

1. 40
2. 30
3. 50
4. 60

  Correct Answer      Choice (3). 50

Explanatory Answer

The count of heads gives the total number of animals / birds as each animal / bird has one head.
Let the number of horses be x.
The remaining will be pigeons. The number of pigeons = (80 - x).
Each pigeon has 2 legs and each horse has 4 legs.
Therefore, total number of legs = 4x + 2(80 - x) = 260
=>4x + 160 - 2x = 260
=>2x = 100
=>x = 50.
x is the number of horses. The number of horses in the farm is 50.

  The correct answer is Choice (3).