There are a total of 738 buffaloes, donkeys, hens and ducks at a farm. The number of hens was 358 more than the number of buffaloes. The total number of donkeys and ducks was 2 times the number of buffaloes.

1. How many donkeys and ducks were there at the farm?
2. The total number of legs for all the donkeys and ducks was 452. How many donkeys were there in the farm?

(a)
Number of buffaloes = 1 u
Number of donkeys and ducks = 2 u
Number of hens = 1 u + 358

Total number of animals
= 1 u + 2 u + 1 u + 358
= 4 u + 358

4 u + 358 = 738
4 u = 738 - 358
4 u = 380

1 u = 380 ÷ 4 = 95

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

(b)

Number of donkeys	Number of donkeys' 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
36	36 x 4 = 144	154	154 x 2= 308	452

Total number of donkeys and ducks = 190

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

Big difference in the total number of legs between the donkeys and the ducks
= 760 - 452
= 308

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

Number of ducks
= 308 ÷ 2 
= 154

Number of donkeys
= 190 - 154
= 36

Answer(s): (a) 190; (b) 36