Profit Percent

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talaangoshtari: Master | Next Rank: 500 Posts; Posts: 154; Joined: Wed May 21, 2014 4:29 amFollowed by: 1 member; Thanked: 8 times

by talaangoshtari » Tue Aug 04, 2015 5:35 am

If 5500 copies of book are published and the transportation cost on them amounts to $82500, then what should be the selling price of the book so that the publisher can earn a profit of 25%? (Transportation cost is 10 percent of the total cost)

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Source: Beat The GMAT — Problem Solving | Tue Aug 04, 2015 5:35 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Aug 04, 2015 5:48 am

talaangoshtari wrote:If 5500 copies of book are published and the transportation cost on them amounts to $82500, then what should be the selling price of the book so that the publisher can earn a profit of 25%? (Transportation cost is 10 percent of the total cost)

Transportation cost per book = (total transportation costs)/(total books) = 82500/5500 = 825/55 = 165/11 = 15.
Since the transportation cost is equal to 1/10 of the total cost, the total cost per book is equal to 10 times the transportation cost:
(10)(15) = 150.
To earn a 25% profit, the price per book must be 5/4 of the total cost per book:
(5/4)(150) = 187.5.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Aug 04, 2015 6:15 am

talaangoshtari wrote:Hi GMATguruNY,

would you please explain why my answer is wrong?

25/100 = (SP - 825000)/825000

SP = 123750

SP for one book = 123750/5500 = 22.5

Your reasoning is fine.
The value in red is incorrect.
One way to solve:

25/100 = (SP - 825000)/825000

1/4 = SP/825000 - 1

5/4 = SP/825000

(5)(825000) = (4)(SP)

(5)(206250) = SP.

SP for one book = (5)(206250)/5500 = 20625/110 = 4125/22 = 375/2 = 187.5.

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