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Question

In a zoo there are some pigeons and some rabbits. If the total number of heads is 300 and the total number of legs is 750, then how many pigeons are there?

A
150
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B
175
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C
200
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D
225
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Solution

The correct option is C 225
Let, the total number of pigeons be p and the total number of rabbits be r
Both the pigeons and rabbits has one head each
so, p+r=300 ...........................................(1)

Each pigeon has two legs and each rabbit has four legs
so, 2p+4r=750................................................(2)

Multiply by (1) by 4
Then 4p+4r=1200................................................(3)

By subtraction (2) from (3)
(4p+4r)(2p+4r)=1200750
4p+4r2p4r=450
2p=450
p=225

Hence, the number of pigeons in the zoo is 225.

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