[Guest]

Selling apples

Two peasants were selling apples in the market. One sold two of them for a coin and the other sold three apples for two coins. Each had thirty apples in her basket. So, the first expected to leave the market with 15 coins and the second with 20 coins.

As they were friends and didn't want to compete, they decided to join the apples and sell them together.

"If I sell three apples for two coins and you sell two for a coin, we should now sell five apples for three coins" they reasoned.

So, they started selling the sixty apples.

Upon having sold all the apples they started sharing the money, the first peasant got her 15 coins and the second got her 20 coins. However, they were surprised to discover they had an extra coin.

How was that possible and how should they share that coin?

P.S.: Sorry if it's a dupe, searching for apples is quite hard in this forum. Also, sorry for the language, it's not my usual limited English vocabulary so I may have misused some words.

[Guest]

The issue is rates of selling, and that 2/1 + 3/2 does not equal 5/3.

If they wanted to split the ratios evenly (and end up with 35 coins), they should take the average of 2/1 and 3/2 and get 7/4.

Who gets the extra coin is a matter of opinion.

[Guest]

Selling apples

Two peasants were selling apples in the market. One sold two of them for a coin and the other sold three apples for two coins. Each had thirty apples in her basket. So, the first expected to leave the market with 15 coins and the second with 20 coins.

As they were friends and didn't want to compete, they decided to join the apples and sell them together.

"If I sell three apples for two coins and you sell two for a coin, we should now sell five apples for three coins" they reasoned.

So, they started selling the sixty apples.

Upon having sold all the apples they started sharing the money, the first peasant got her 15 coins and the second got her 20 coins. However, they were surprised to discover they had an extra coin.

How was that possible and how should they share that coin?

P.S.: Sorry if it's a dupe, searching for apples is quite hard in this forum. Also, sorry for the language, it's not my usual limited English vocabulary so I may have misused some words.

I haven't heard this one before but I haven't combed the archives looking.

The extra coin comes from the uneven rate that they were selling the apples. Each time they sold 5 apples for 3 coins, Peasant 2 was selling 3 apples to Peasant 1's 2 apples. Thus after 10 transactions, P2 has sold all of her apples (10 transactions x 3 apples/transaction = P2's 30 apples). But they keep selling P1's last 10 apples at the increased price. So Peasant 1 should get the extra coin since she effectively raised her prices.

[Guest]

this is similar to other ones posted

if you turn these into coints per apple you get

3 apples for 2 coins = 0.66 etc.. coins per apple

2 apples for 1 coin = 0.5 coins per apple

if you split these evenly you should get approximately 7 apples for 4 coins

[Guest]

Who gets the extra coin is a matter of opinion.

The issue is rates of selling, and that 2/1 + 3/2 does not equal 5/3.

If they wanted to split the ratios evenly (and end up with 35 coins), they should take the average of 2/1 and 3/2 and get 7/4.

60 apples / (7apples/4coins) = 34 2/7 coins... assuming your actually selling 1 apple for 4/7 of a coin (because 7 doesn't go into 60 evenly)

[Guest]

In the first case the average price of an apple is:

P1=(0.5x30+(2/3)x30)/60=0.583

In the second case each apple costs P2=3/5=0.6.

So the higher cost of each apple is

P2 - P1 = 0.6 - 0.583 = 0.017.

0.017x60 = 1 (approximate), which explains the extra coin. It can be divided in proportion to the original cost of apples (0.5 and 0.6), so the first gets 0.45 and the second 0.55.

[Guest]

In the first case the average price of an apple is:

P1=(0.5x30+(2/3)x30)/60=0.583

In the second case each apple costs P2=3/5=0.6.

So the higher cost of each apple is

P2 - P1 = 0.6 - 0.583 = 0.017.

0.017x60 = 1 (approximate), which explains the extra coin. It can be divided in proportion to the original cost of apples (0.5 and 0.6), so the first gets 0.45 and the second 0.55.

well done zoris just expanded after my answer

[Guest]

You've understood the problem, but no one has yet correctly established what would be the fair money distribution.

Edited April 9, 2008 by Thanshin

[Guest]

this is similar to other ones posted

if you turn these into coints per apple you get

3 apples for 2 coins = 0.66 etc.. coins per apple

2 apples for 1 coin = 0.5 coins per apple

if you split these evenly you should get approximately 7 apples for 4 coins

another answer of 7 apples for 4 coins. What you guys are doing is averaging apples/coin... and if you multiply 7apples/4coins x 35 coins (or 4coins/7apples x 60 apples) you get a non whole number... Which confuses me. I can't see why that wouldn't work.

Now if you average coins/apple, you see that (1/2 + 2/3)/2 = (3/6 + 4/6)/2 = (7/6)/2 = 7/12 = 35 coins/60 apples

[Guest]

You've understood the problem, but no one has yet correctly established what would be the fair money distribution.

ok...

if its the fair money distibution then we've got to work out how much each was selling their original apples for

Peasant 1 0.666 etc.. apples per coin

Peasant 2 0.5 apples per coin

put this into a ratio 4:3 for every 4 coins Peasant 1 gets Peasant 2 gets 3. 36/7

Peasant 1 = 4 "parts" x 5.143 = 20.571 coins

Peasant 2 = 3 "parts" x 5.143 = 15.429 coins

P.S. i have rounded all valued to 3 d.p.

[Guest]

You've understood the problem, but no one has yet correctly established what would be the fair money distribution.

I thought I explained that peasant 1 gets the extra coin because she effectively raised her price.

[Guest]

I must go home now, so I'll post the solution to avoid leaving you with the doubt all night:

The first peasant sold an apple for 0,5 coins.

The second for 0,666... coins.

Joined, they sold the apples for 0,6 coins.

The first peasant wins money:

30 apples * (0.6 - 0.5) = 3 coins

The second peasant loses money:

30 apples * (0.6 - 0.666...) = 2 coins.

Which means the first peasant owes the second the extra coin and two more coins.

[Guest]

I must go home now, so I'll post the solution to avoid leaving you with the doubt all night:

The first peasant sold an apple for 0,5 coins.

The second for 0,666... coins.

Joined, they sold the apples for 0,6 coins.

The first peasant wins money:

30 apples * (0.6 - 0.5) = 3 coins

The second peasant loses money:

30 apples * (0.6 - 0.666...) = 2 coins.

Which means the first peasant owes the second the extra coin and two more coins.

You're saying that after they sell the apples that Peasant 1 is going to make two coins less than she normally would and Peasant 2 is going to make 3 coins more!!!

I think I see the flaw in your math/explanation! If Peasant 1 sells 30 apples at 3/5 (.6) she'll make 18 coins, 3 more than she normally would. Peasant 2 would also make 18 coins, 2 less than she normally would. So Peasant 1 would give Peasant 2 two coins to bring her up to the 20 coins leaving Peasant 1 with an "extra" coin. This point with Peasant 2 with 20 coins, Peasant 1 with 15 coins, and an "extra" coin is where the original problem leaves us. The question is what to do with the extra coin. I still think that Peasant 1 should keep it since she ended up raising her prices more than Peasant 2 lowered hers. But they're friends (or they wouldn't have done this in the first place) so they might use some other rational... perhaps split a beer on the way home!

[Guest]

You're saying that after they sell the apples that Peasant 1 is going to make two coins less than she normally would and Peasant 2 is going to make 3 coins more!!!

I think I see the flaw in your math/explanation! If Peasant 1 sells 30 apples at 3/5 (.6) she'll make 18 coins, 3 more than she normally would. Peasant 2 would also make 18 coins, 2 less than she normally would. So Peasant 1 would give Peasant 2 two coins to bring her up to the 20 coins leaving Peasant 1 with an "extra" coin. This point with Peasant 2 with 20 coins, Peasant 1 with 15 coins, and an "extra" coin is where the original problem leaves us. The question is what to do with the extra coin. I still think that Peasant 1 should keep it since she ended up raising her prices more than Peasant 2 lowered hers. But they're friends (or they wouldn't have done this in the first place) so they might use some other rational... perhaps split a beer on the way home!

I have to agree with redshift here. If you read my earlier posts then you will see that i have taken that ratios of each peasant and found them out for 61 coins

Edited April 12, 2008 by andreay