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A person buys some Apples and Mangoes

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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A person buys some Apples and Mangoes

by AJWILL » Sat Aug 04, 2012 1:28 pm
A person buys some Apples and Mangoes from the market. Cost price of a Mango is twice that of an Apple and the selling price is thrice that of an Apple. The selling price of apple is twice the cost price of apple and he makes the profit of 150 % on the whole. What is the ratio of number of mangoes to the number of apples ?

[A] 3:5

3:4

[C] 1:2

[D] 2:3

[E] 2:5


Correct Answer : C
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by eagleeye » Sat Aug 04, 2012 1:39 pm
AJWILL wrote:A person buys some Apples and Mangoes from the market. Cost price of a Mango is twice that of an Apple and the selling price is thrice that of an Apple. The selling price of apple is twice the cost price of apple and he makes the profit of 150 % on the whole. What is the ratio of number of mangoes to the number of apples ?

[A] 3:5

3:4

[C] 1:2

[D] 2:3

[E] 2:5


Correct Answer : C


Since everything is in terms of the apple. Let cost of one apple be 1.
Then selling price of apple = 2*1=2 .
Also, cost of mango = 2*1=2,
and selling price of mango = 3*2 = 6
Profit on an apple =2-1 = 1
Profit on a mango = 6-2 = 4

Now let's say he sells m mangoes and a apples, then
150% = (Total profit)/(Total cost) = (4m+a)/(2m+a)
3/2 = (4m+a)/(2m+a)
=> 6m+3a = 8m+2a
=> 2m = a
=> m/a = 1/2 => m:a = 1:2

C is correct. :)
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by AJWILL » Sat Aug 04, 2012 1:50 pm
thanks for prompt reply.

m just stuck at "he makes the profit of 150 % on the whole." statement n how u converted it into 150% = (Total profit)/(Total cost) equation.

m sure it must be something very basic but i am missing that basic link..
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by eagleeye » Sat Aug 04, 2012 2:05 pm
AJWILL wrote:thanks for prompt reply.

m just stuck at "he makes the profit of 150 % on the whole." statement n how u converted it into 150% = (Total profit)/(Total cost) equation.

m sure it must be something very basic but i am missing that basic link..
First off, and this is besides the point, this question never says that the person actually managed to sell all the fruits. If it were an option, I would have picked "cannot be determined from the data provided". Anyway, we can see that author assumes that the person managed to sell all his fruit at a profit after buying.

Now definition of profit = Selling price - cost price.
Definition of profit% = 100% * (profit)/(cost price).

In this case, the person buys the fruit at a certain cost, and then sells it all. Hence overall profit% refers to the Total money he made as a percentage of the Total money he spent to buy the fruit in the first place.

So , I wrote 150% = (Total profit)/(Total cost).

Is it clear now?
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by AJWILL » Sat Aug 04, 2012 2:12 pm
AWESOME!!

gotcha

thank you
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