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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

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Solution:
Option(C) is correct

Heads Count = 200.

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 $\dfrac{11\times 200}{20}$

$= \textbf{110 Piegons.}$