There are a total of 644 sheep, buffaloes, hens and ducks at a farm. The number of hens was 350 more than the number of sheep. The total number of buffaloes and ducks was 4 times the number of sheep.

1. How many buffaloes and ducks were there at the farm?
2. The total number of legs for all the buffaloes and ducks was 598. How many buffaloes were there in the farm?

(a)
Number of sheep = 1 u
Number of buffaloes and ducks = 4 u
Number of hens = 1 u + 350

Total number of animals
= 1 u + 4 u + 1 u + 350
= 6 u + 350

6 u + 350 = 644
6 u = 644 - 350
6 u = 294

1 u = 294 ÷ 6 = 49

Number of buffaloes and ducks
= 4 u
= 4 x 49
= 196

(b)

Number of buffaloes	Number of buffaloes' legs	Number of ducks	Number of ducks' legs	Total
196	196 x 4 = 784	0	0	784
195	195 x 4 = 780	1	1 x 2 = 2	782
103	103 x 4 = 412	93	93 x 2= 186	598

Total number of buffaloes and ducks = 196

Total number of legs if all of them are buffaloes
= 196 x 4 
= 784

Big difference in the total number of legs between the buffaloes and the ducks
= 784 - 598
= 186

Small difference in number of legs between one buffalo and one duck
= 4 - 2 
= 2

Number of ducks
= 186 ÷ 2 
= 93

Number of buffaloes
= 196 - 93
= 103

Answer(s): (a) 196; (b) 103