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by govind_raj_76 » Thu Jun 03, 2010 8:19 pm
Mr. Potter sells three producrs A, B and C. He earns different amount of profit from each of them. Among the products A, B and C, which one of them definitely does not earn Mr. Potter the maximum profit ?

1) The Selling price of A, B and C are in the ratio of 4:6:5

2) The Cost price of A, B and C are in the ratio of 3:5:4

Please help. Thanks,
Govind
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by Rahul@gurome » Thu Jun 03, 2010 9:33 pm
Obviously, both statements alone are not sufficient to answer the question because we need to know both selling price and cost price to know about the profit.
Let us check on combining both the statements.

Let the SP be 4x,6x and 5x and CP be 3y,5y and 4y for A, B and C respectively.
The profits are therefore 4x-3y, 6x-5y,5x-4y.
We need to know that which of them cannot take the maximum possible value?
Now if we arrange the three values 4x-3y, 6x-5y,5x-4y in descending order we can have 3! Or 6 arrangements.
(1) 4x-3y>6x-5y>5x-4y
(2) 4x-3y>5x-4y>6x-5y
(3) 6x-5y>5x-4y>4x-3y
(4) 6x-5y>4x-3y>5x-4y
(5) 5x-4y>4x-3y>6x-5y
(6) 5x-4y>6x-5y>4x-3y

We next check the validity of each of the arrangements.
(1) means 4x-3y>6x-5y and 6x-5y>5x-4y
which is 2y>2x and x>y - not possible.
(2) means 4x-3y>5x-4y and 5x-4y>6x-5y
which is y>x and y>x - possible.
(3) means 6x-5y>5x-4y and 5x-4y>4x-3y
which is x>y and x>y - possible.
(4) means 6x-5y>4x-3y and 4x-3y>5x-4y
which is 2x>2y and y>x - not possible
(5) means 5x-4y>4x-3y and 4x-3y > 6x-5y
which is x>y and 2y>2x - not possible.
(6) means 5x-4y>6x-5y and 6x-5y>4x-3y
which is y>x and 2x>2y - not possible.

Since (5) and (6) are not possible, 5x-4y can never take the maximum possible value
Or C can never give the maximum profit.

On combining both the statements we can get an answer.

The correct answer is (C).
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by krazy800 » Thu Jun 03, 2010 9:34 pm
govind_raj_76 wrote:Mr. Potter sells three producrs A, B and C. He earns different amount of profit from each of them. Among the products A, B and C, which one of them definitely does not earn Mr. Potter the maximum profit ?

1) The Selling price of A, B and C are in the ratio of 4:6:5

2) The Cost price of A, B and C are in the ratio of 3:5:4

Please help. Thanks,
IMO C

profit = selling price - cost price

Statement 1: cost price info not given: insufficient

Statement 2: selling price info not given: insufficient

Combining statement 1 & 2 we can determine the one which has minimum profit

here is how:

Let total selling price = S
Cost price = C

A's profit = 4/15(S) - 3/12 (C) = (1/4)* (S-C) (approximately)
C's profit = 5/15 (S) - 4/12 (C) =1/3* (S-C)
B's profit = (1-(1/4)-(1/3)) * (S-C)

therefore A doesn't earn maximum profit


HTH!
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