There are a total of 793 donkeys, buffaloes, geese and hens at a farm. The number of geese was 349 more than the number of donkeys. The total number of buffaloes and hens was 4 times the number of donkeys.

1. How many buffaloes and hens were there at the farm?
2. The total number of legs for all the buffaloes and hens was 636. How many buffaloes were there in the farm?

(a)
Number of donkeys = 1 u
Number of buffaloes and hens = 4 u
Number of geese = 1 u + 349

Total number of animals
= 1 u + 4 u + 1 u + 349
= 6 u + 349

6 u + 349 = 793
6 u = 793 - 349
6 u = 444

1 u = 444 ÷ 6 = 74

Number of buffaloes and hens
= 4 u
= 4 x 74
= 296

(b)

Number of buffaloes	Number of buffaloes' legs	Number of hens	Number of hens' legs	Total
296	296 x 4 = 1184	0	0	1184
295	295 x 4 = 1180	1	1 x 2 = 2	1182
22	22 x 4 = 88	274	274 x 2= 548	636

Total number of buffaloes and hens = 296

Total number of legs if all of them are buffaloes
= 296 x 4 
= 1184

Big difference in the total number of legs between the buffaloes and the hens
= 1184 - 636
= 548

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

Number of hens
= 548 ÷ 2 
= 274

Number of buffaloes
= 296 - 274
= 22

Answer(s): (a) 296; (b) 22