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. $150$
• B. $175$
• C. $200$
• D. $225$

Answer 1

Answer: (D)

$225$

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)

$(4p+4r)-(2p+4r)=1200-750$

$\Rightarrow 4p+4r-2p-4r=450$

$\Rightarrow 2p=450$

$\Rightarrow p=225$

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