# Find the number of animals and their kind

My friend who owns a farm near Bangalore has five droves of animals on his farm consisting of cows, sheep and pigs with the same number of animals in each drove.

One day he decided to sell them all and sold them to eight dealers.

Each of the eight dealers bought the same number of animals and paid at the rate of Rs. 17 for each cow, Rs. 2 for each sheep and Rs. 2 for each pig.

My friend recieved from the dealers in total Rs. 301.

How many animals in all did he have and how many of each kind?

We know that there were five droves with an equal number in each drove, and therefore the number must be divisible by 5. As every one of the eight dealers bought the same number of animals, the number must also be divisible by 8. This leads us to the conclusion that the number must be a multiple of 40.

Now the highest possible multiple of 40 that will work will be found to be 120, and this number could be made up in one of two ways—1 cow, 23 sheep and 96 pigs or 3 cows, 8 sheep and 109 pigs. But the first does not fit in because the animals consisted of ‘Cows, Sheep and Pigs’ and a single ‘Cow’ is not ‘Cows’. Therefore the second possibility is the correct answer.

### Your Answer

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