In competitive exam, counting number of heads and legs of animals in farm is a famous and most common type of problem. Aspirants may find it difficult but is the most easiest topic of reasoning. So in this article we will try to understand how to solve number of heads and legs problems in less than 10 seconds.

Let us understand it with the help of example:-

**Question:-**

**In a farm there are some cows and birds. If there are total 35 heads and 110 legs then how many cows and birds are there?**

No need to assume ‘x’ and make any equations. This a standard question in various exams. So we need a short cut to save our time in exam halls.

**Short cut**:-Just halve the given number of legs and subtract from it the number of heads. You will get the number of four legged animal. In this case (110÷2=55), 55-35= 20 (is four legged animal i.e. cows).

You will get two legged animals by subtraction total animal in farm by four legged animals. In this case 35-20= 15. So there are 15 birds and 20 cows in the farm.

See, how easy it is to solve question like this where we have to find total number of legs or heads of the animals/birds present in the farm. You will hardly take more than 10-20 second to solve these types of questions.

You can also these type of questions using concept of Mixture and alligations.

**In a farm there are some cows and birds. If there are total 35 heads and 110 legs then how many cows and birds are there?**

If we assumed all the animals are four legged then we should have 140 legs and if we assume all the animals are two legged we should have 70 legs. But in reality we have 110 legs. By using mixture and allegation we can get the ratio of two legged animals and four legged animals and can solve question easily.

Carefully observe the solution given below.

We can say there number of two legged animals and four legged animals are in the ration of 3:4 which means if there are 3 two legged animals then there will be 4 four legged animals. By this method we have 7 animals in farm but in reality there are 35 animals. So 1 unit of ratio is representing 5 real animals so we can easily calculate number of two legged or four legged animal.

We have 3 unit ratio for two legged animal and one unit is representing 5 animals so there are total 15 two legged animals i.e. birds.

We have 4 unit ratio for four legged animals and one unit is representing 5 animals so there are total 20 four legged animals i.e. cows.

So we can say there are 20 cows and 15 birds in the farm.

You can use any of the above mention method to solve these types of questions and both methods are very easy. It may seem lengthy but I have to explain everything to you in writing so it may seem lengthy but with practice it will not take more than 20 seconds to solve number of heads and legs problems in various competitive exams.

To solve these types of questions as fast as possible depends on your speed of understanding the question and applying the above mentioned method to solve these type of questions.

**Solve these number of heads and legs problems by yourself to have command over this concept and topic. **

**1.) If there are 18 heads and 48 legs of humans and horses, find the number of humans and horses respectively:**

a.) 12, 8

b.) 10, 8

c.) 11, 7

d.) 12, 6

**2.) There are 108 legs and 33 heads in the farm. There are only chicken and rabbits in his farm. How many chickens are there in the farm?
**a.) 21

b.) 12

c.) 15

d.) 18

**3.) A man has some hens and cows. If the number of heads be 48 and the number of feet equals 14o, then the number of hens will be :**

a.) 22

b.) 24

c.) 26

d.) 28

Type your answer in the comment section below. Feel free to share your opinion as well.

You have understand one thing as well that in this world there is nothing like “one shoe fits all” and the method we have explained you above is no exception to this universal harsh reality it will solve most of your questions but in some question you have to use basic method to solve these types of question using equations.