My blog has moved!

You should be automatically redirected in 6 seconds. If not, visit
and update your bookmarks.

The Right Place For Online Math Help |

Kathy and Jane were selling sweets in the market place. Kathy at 3 for a dollar and Jane at 2 for a dollar. One day both of them were obliged to return home when each had thirty sweets unsold. They put together the two lots of sweets and and handing them over to a friend, asked her to sell them at 5 for two dollars. According to their calculation, after all, 3 for 1 dollar and 2 for 1 dollar was exactly same as 5 for 2 dollars.

Now they were expecting to get 25 dollars for the sweets as they would have got, if sold separately. But much do their surprise they got only 24 dollars for the entire lot.

Now where did the 1 dollar go? Their friend was a cheat?

There isn't really any mystery. While the two ways of selling are only identical, when the number of sweets sold at 3 for 1 dollar and 2 for 1 dollar is in proportion of 3:2. So , if Kathy had sold 36 sweets and Jane 24, they would have fetched 24 dollars (12 dollars each) , immaterial of, whatever sold separately or at 5 for 2 dollars. But if they had the same number of sweets which led to loss of 1 dollar when sold together, in every 60 sweets. So if they had 60 each (120 altogether) , there would be a loss of 2 dollars and so on.

In the case of 60, the missing 1 dollar arises from the fact that Kathy gains 2 dollars and Jane losses 3 dollars(If they share $12 each).

Kathy receives $9.5 and Jane $14.5, so that each loses $.50 in the transaction.


  1. Henry said...
    I've seen similar question about the missing 1 dollar...

    Here's how it goes:

    three students want to share a room in a hotel for the night. It costs $300 per room, so they each payed $100 to the agent.

    the agent then took the money to the manager. The manager gave the agent $50 back for student discount. So the agent walks back with the money, thinking he can't divide that money equally to the three students, so he took $20 for himself, and decides not to tell the students. He then gave $30 back to the students, which each recieved $10 back.

    This means the students first payed $100 - $10 = $90
    and the agent took $20

    Here's the question...
    $90 + $90 + $90 = $270
    (from each student)
    $270 + $20 = $290
    (added to the money stolen from agent)

    so where's the missing $10 ??

    Interesting maths blog...
    you can visit my jokes blog too if you want to have a laugh~
    Anonymous said...
    so I cant figure this out, if someone could help here it is.

    Lucy borrows $50 from one friend.
    She then Borrows $50 from another, for a total of $100.
    Lucy Purchases something at the price if $97. for a total of $3 in change. She gives the first friend one dollar, than the second a dollar, therefor owing them each 49 dollars. so when you add it together 49 + 49 = $98 you then include the dollar she kept for herselfso, $98 + $1 = $99, where did the missing the dollar go?
    Math said...
    Anony I have already posted a similar puzzle here

    Actually Lucy borrowed $49+$49=$98 from the two friends and she spent $97.
    she has one dollar with her.
    So, it is $97+$1=$98.
    Anonymous said...
    I understand how this works but my teacher wants me to explain it in "plain english" with no math calculations and no mention of average prices. i am having trouble trying to explain it :(
    Anonymous said...
    ok now i get it its because it takes more transactions to sell at 2 for 1 than at 3 for 1 so in order for the to be sold together 36 will be sold at 3 for 1 and 24 will be sold at 2 for therfore the loss on selling the 6 sweets at 3for1 insteads of 2 for 1 will be $1 :):)

Post a Comment