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Cows and buffaloes. (Posted on 2015-01-07) Difficulty: 2 of 5
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.

See The Solution Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution 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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