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Question 923626: A man bought some oranges at the rate of 3
oranges for one rupee and equal number of oranges
at the rate of 2 oranges for one rupee. What is his
profit, if he sells 2 oranges for one rupee.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! he buys a batch of oranges at 3 oranges per rupee.
his cost per orange is equal to 1/3 of a rupee.
he buys another batch of oranges at 2 oranges per rupee.
his cost per orange is equal to 1/2 of a rupee.
since he buys an equal amount of each, then his average cost per orange for both batches is equal to (1/3 + 1/2) / 2 which is equal to 5/6 divided by 2 which is equal to 5/12 of a rupee.
his cost for 2 oranges is therefore equal to 10/12 of a rupee which can be simplified to 5/6 of a rupee.
if he sells 2 oranges for 1 rupee, then his profit is 1 - 5/6 = 1/6 of a rupee.
we can test this to see if it makes sense.
assume he buys 2 batches of 18 oranges apiece.
one batch is bought at 3 oranges per rupee for a total cost of 6 rupees.
the other batch is bought at 2 oranges per rupee for a total cost of 9 rupees.
his total cost is equal to 6 + 9 = 15 rupees.
his cost per orange is equal to 15 / 36 = 5/12 of a rupee per orange.
he sells 2.
he makes 1 rupee.
his cost is 10/12 of a rupee which simplifies to 5/6 of a rupee.
his profit is 1 rupee minus 5/6 of a rupee = 1/6 of a rupee.
solution is confirmed as good.
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