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 Cows and buffaloes. (Posted on 2015-01-07)
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.

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 Buffalo milk? (spoiler) Comment 2 of 2 |
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
 Posted by Steve Herman on 2015-01-07 10:45:17

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