A dairy farm's cattle consists of 75% cows and 25% buffaloes.

Exactly 80% of all these animals are producing milk.

There are 76 milk-producing cows in the farm.

The above data defines uniquely the total number of animals in the farm.

What is it?

This is an old problem from Hindu Math. sources.

Let t = total animals

if 75% are buffalo, then t is a multiple of 4

if 80% are milking, then t is a multiple of 5

So t is a multiple of 20

Number of cows = 3t/4 >= number of milk cows = 76

So t >= 101 + 1/3

If we were confident that there was only one answer, we could stop now. t = 120 would be the answer.

But let's check.

Number of buffalo = t/4 >= number of milk buffalos = (4t/5 - 76)

76 > 11t/20

t< 138.18

So yes, t = 120

90 cows, of which 76 milk

30 buffalo, of which 20 milk

*Edited on ***January 7, 2015, 11:02 am**