There are a total of 687 horses, buffaloes, hens and ducks at a farm. The number of hens was 307 more than the number of horses. The total number of buffaloes and ducks was 2 times the number of horses.

1. How many buffaloes and ducks were there at the farm?
2. The total number of legs for all the buffaloes and ducks was 508. How many buffaloes were there in the farm?

(a)
Number of horses = 1 u
Number of buffaloes and ducks = 2 u
Number of hens = 1 u + 307

Total number of animals
= 1 u + 2 u + 1 u + 307
= 4 u + 307

4 u + 307 = 687
4 u = 687 - 307
4 u = 380

1 u = 380 ÷ 4 = 95

Number of buffaloes and ducks
= 2 u
= 2 x 95
= 190

(b)

Number of buffaloes	Number of buffaloes' legs	Number of ducks	Number of ducks' legs	Total
190	190 x 4 = 760	0	0	760
189	189 x 4 = 756	1	1 x 2 = 2	758
64	64 x 4 = 256	126	126 x 2= 252	508

Total number of buffaloes and ducks = 190

Total number of legs if all of them are buffaloes
= 190 x 4 
= 760

Big difference in the total number of legs between the buffaloes and the ducks
= 760 - 508
= 252

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

Number of ducks
= 252 ÷ 2 
= 126

Number of buffaloes
= 190 - 126
= 64

Answer(s): (a) 190; (b) 64