

Direct Formula / Rule 14 :
Theorem:
In a group, there are some 4legged creatures
and some 2legged creatures. If heads are counted, there
are x and if leggs are counted there are y,
then the no. of 4legged creatures are given by
or = 
( 
Total legs  2 X Total heads 
) 
and 
2 
the no. of 2legged
creatures are given by
or = 
( 
4 X Total heads  Total legs 
) 
and 
2 
Example :
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?
Detail Method :
Let the no. of rabbits be R and the pigeons be P.
According to the question
R + P = 200 ....(i) and
4R + 2P = 580 .... (ii)
[so Rabbits are 4legged creatures and pigeons are 2legged creatures.]
From solving eqn (i) and (ii) we get
R = 90, and P = 110
No. of rabbits = 90 and
No. of pigeons = 110.
Ailigation Method :
Rule of Alligation is applicable
on number of legs per head.
Average number of legs per head = 
580 
= 
29 
200  10 
= Rabbit : Pigeons = 9 : 11
So number of pigeons = 
200 
X 11 = 110 
9 + 11 
Quicker Method : Here you can use direct formula :
the number of pigeons (2legged) = 
4 X 200  580 
= 110 
2 
Exercise :

In a courtyard there are many chickens and goats. If
heads are counted, it comes to 100 but when legs are
counted, it comes to 320. Find the number of chickens
and goats in the courtyard.

In a zoo, there are rabbits and pigeons. lf heads are
counted, there are 100 and if legs are counted, there are
290. How many rabbits are there?

In a zoo, there are rabbits and pigeons. If heads are
counted, there are 50 and if legs are counted, there are
140. How many pigeons are there?
Answers :
1 = 40, 60, 2 = 45, 3 = 30



