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# cows problem

## Question

Four black cows and three brown cows give as much milk in five days as three black cows and five brown cows give in four days. Which color cow gives the most milk?

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Four black cows and three brown cows give as much milk in five days as three black cows and five brown cows give in four days. Which color cow gives the most milk?

Brown cows give more. in the ratio of 8 to 5.

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Brown cows produce more milk. (8/5 times more)

My reasoning

days = d

Black cows = l

Brown cows = r

5d(4l + 3r) = 4d(3l + 5r)

20dl + 15dr = 12dl + 20dr

20dl - 12dl = 20dr - 15dr

8dl = 5dr

8l = 5r

Therefore we would need 8 black cow to give the same amount of milk as 5 brown cows.

(Been a while since I was in school but i think the above is correct.

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Mathematical Solution: 1 black cow gives A liter milk in one day, one brown cow B liter.

4 black cows and 3 brown cows will give 4*5A+3*5B liter milk in 5 days.

And 3 black + 5 brown cows will give 3*4A+5*4B liter in 4 days.

Both are equal as per OP. So 4*5A+3*5B=3*4A+5*4B

8A=5B Therefore B > A

Logical Solution: Let us assume both – black & brown - cows gave equal milk in one day.

Then from first statement 7 cows in 5 days give as much milk as from second statement 8 cows give in 4days. So number of cows increased is only ONE (brown cow) which APPARENTLY gave as much milk in 4 days as given by 7 cows in one day.

From above it is clear that Brown cow gives more milk than black cow.

Edited by bhramarraj
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Mathematical Solution: 1 black cow gives A liter milk in one day, one brown cow B liter.

4 black cows and 3 brown cows will give 4*5A+3*5B liter milk in 5 days.

And 3 black + 5 brown cows will give 3*4A+5*4B liter in 4 days.

Both are equal as per OP. So 4*5A+3*5B=3*4A+5*4B

8A=5B Therefore B > A

Logical Solution: Let us assume both – black & brown - cows gave equal milk in one day.

Then from first statement 7 cows in 5 days give as much milk as from second statement 8 cows give in 4days. So number of cows increased is only ONE (brown cow) which APPARENTLY gave as much milk in 4 days as given by 7 cows in one day.

From above it is clear that Brown cow gives more milk than black cow.

That's it... all of you had got the correct answer...

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