# Easy Alligations or Mixtures Solved QuestionAptitude Discussion

 Q. In a zoo, there are Rabbits and Pigeons. If heads are counted, there are 200 and if legs are counted, there are 580. How many pigeons are there?
 ✖ A. 90 ✖ B. 100 ✔ C. 110 ✖ D. 120

Solution:
Option(C) is correct

Legs count = 580.

As we know that average legs per head for rabbit, $R =4$ and average legs per head for pigeon, $P =2$.

Now, average Legs count per head,

$= \dfrac{580}{200} = \dfrac{29}{10}$.

Rabbit, $R$                         Pigeon, $P$

4                                           2

\                               /

mean

$\dfrac{29}{10}$

/                           \

$\left(\dfrac{29}{10}-2\right)$         :          $\left(4-\dfrac{29}{10}\right)$

$\dfrac{9}{10}$                                   $\dfrac{11}{10}$

$\dfrac{R}{P}= \dfrac{(9/10)}{(11/10)}$

$\Rightarrow R:P= 9 : 11$.

Thus, number of piegons,

$P=\dfrac{11}{11+9} \times 200$

$=\dfrac{11}{20} \times 200$

$= \textbf{110 pigeons}$

Edit: Thank you SriPavani for alternate calculation in the comments.

Edit2: To arrive at the answer using a different approach ( using Algebra) please check KARTIK's comment.

Edit 3: For yet another alternative solution using algebraic equations, check comment by Sanket Singh.

Edit 4: For yet another alternative solution using optimised algebraic equations (only 1 variable), check comment by SIDHARTH KUMAR DAS.

Edit 5: Yet another solution by Shreya and Shubham.

## (8) Comment(s)

Shubham
()

200*2=400,

580-400=180,

no. of extra rabit need to complete the count is 180/2=90

therefore no. of piegion

Shubham
()

$200*2=400$,

$580-400=180$,

Number of extra rabbits need to complete the count is,

$\dfrac{180}{2}=90$

Therefore number of pigeons,

$=200-90$

$=110$

KVS VIRINCHI
()

Its simple and easy way to solve..I THOUGHT OF IT

Shreya
()

$2*200=400$

$580-400 =180$

This 180 is extra legs so $180/2 = 90$

This is number of rabbits .

$200-90$

$= 110$ number of piegons.

SIDHARTH KUMAR DAS
()

Let, the number of pigeons be $x$, then the number of rabbits are $200-x$

Pigeons have 2 legs, while rabbits have 4.

atq,

$2x +4(200-x) =580$

$=>x=110$ (Ans.)

Sanket Singh
()

Let no. of rabbits be $R$ and no. of pigeons be $P$

$4R+2P= 580$ & $R+P=200$

On solving above;

$R=90$ & $P=110$ Ans.

KARTIK
()

One more way of solving this type of question.

no. of rabbits $= r$

no. of pigeons $= p$

$r+p = 200$

also,

$4r+ 2p = 580$

Solving above equation for $p$

we get

$2p = 220$

$p = 110$ :)

SriPavani
()

Assuming that all are pigeons then total pigeons leg count will be 200*2(legs) = 400 legs.

and all are Rabbits then total Rabbit's leg count will be 200*4(legs) = 800 legs.

400             800

\              /

580(Given)

/            \

800-580       580-400
=220           =180

Ratio $= 11:9$

Ratio Sum $11+9=20$ which is given as $200$

So 11 parts will be $\dfrac{11\times 200}{20}$

$= \textbf{110 Piegons.}$