In a market Mrs. Smith and Mrs. Jones sell apples. Mrs. Jones sells her apples for two per shilling. The apples of Mrs. Smith are a bit smaller; she sells hers for three per shilling.
At a certain moment, when both ladies both have the same number of apples left, Mrs. Smith is called away. She asks her neighbour to take care of her goods.
To make everything less complicated, Mrs. Jones simply puts all apples to one big pile, and starts selling them for two shilling per five apples. When Mrs. Smith returns the next day, all apples have been sold. But when they start dividing the money, there appears to be a shortage of seven shilling.
Supposing they divide the number equally, how much does Mrs. Jones lose with this deal?
(In reply to
answer by K Sengupta)
Let the # applesleft in each of the respective inventories of Mrs. Smith and Mrs. Jones be x.
The cost price of each apple for Mrs. Smith = 1/2 shilling
The cost price of each apple for Mrs. Jones = 1/3 shilling
Now, thr price at which Mrs. Jones sold the leftover joint stock of x+x=2x apples is 2/5 shilling/apple
Now, the income from the joint stock of 2x apples at normal prices would have been (x/2+x/3)= 5x/6 shillings.
IIn reality, however, the actual income of Mrs. Jones by selling 2x apples @ 2/5 shlling/apple is 4x/5 shillings.
Therefore, loss incurred st the said transaction = 5x/6 -4x/5 = x/30 shillings.
Accordingly, we must have:
x/30=7, giving: x=210
Thus, the total income by selling the joint stock of apples at the reduced price of 2/5 shilling/apple =4x/5 shillings=(4*210)/5 = 168 shillings.
Mrs. Jones' share in this transaction = 168/2 = 84 shillings.
If Mrs. Jones had sold her stock of 210 apples @ 1/2 shillings/apple, she would have received 210/2=105 shillings.
Consequently, Mrs. Jones lost 105-84=21 shillings in the said transaction.
Edited on December 25, 2021, 6:10 am
Puzzle Solution
