a milkman has some buffaloes,cows and goats.he has goats eqal to 5/2 times the number of cows and cows equal to 3/2 times the number of buffaloes.if there are 150 animals with the milkman how many of each category does he have with him

Answer : 

Let Total number of Goats  =  x 
Total number of Cows  =  y
And
Total number of  buffaloes =  z 
So, 

x + y + z  =  150                              --------------- ( 1)

And As given ​goats equal to $\frac{5}{2}$ times the number of cows ,
So,
x  = $\frac{5}{2}$ y                                         --------------- ( 2 )
And
Cows equal to $\frac{3}{2}$ times the number of buffaloes
SO,
y  = $\frac{3}{2}$ z                                        --------------- ( 3 )
And
z  = $\frac{2}{3}$y                                        --------------- ( 4 )

Now from equation 2 and 4 we substitute values in equation 1 , and get 


 $\frac{5}{2}$ y + y + $\frac{2}{3}$y =  150  

Now taking LCM 

$\frac{15 y + 6y + 4y}{6}$  =  150

25y  = 900

y  = 36   , Substitute that value in equation 2 and 4 , we get 

x  = $\frac{5}{2}$ ( 36 )   = 5 $\times$ 18  =  90 
And
z = $\frac{2}{3}$ ( 36 )  = 2 ​$\times$  12  =  24 
So,
Milkman have , Total number of Goats  =  90
Total number of Cows  =  36
And
Total number of  buffaloes =  24                                                                       ( Ans )