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In a Zoo; there are rabbits and pigeons. If heads are counted, there are 120 and if legs are counted, there are 340. How many rabbits are there?

In a Zoo; there are rabbits and pigeons. If heads are counted, there are 120 and if legs are counted, there are 340. How many rabbits are there? Correct Answer 50

Given:

There are rabbits and pigeons. If heads are counted, there are 120 and if legs are counted, there are 340

Concept:

 A Rabbit has 4 legs and a Pigeon has 2 legs. Both rabbit and Pigeon has 1 head only

Calculation:

Let x be the number of Rabbits

Number of Pigeons = 120 - x (∵ Total heads are 120 means Total number of rabbits and Pigeons = 120)

If Legs are counted, 340 means total legs = 340

 A Rabbit has 4 legs and a Pigeon has 2 legs

⇒ 4x + (2 × (120 - x)) = 340

⇒ 4x + 240 - 2x = 340

⇒ 2x = 100

⇒ x = 50

Number of Rabbits = 50

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