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coolgirl26: Senior | Next Rank: 100 Posts; Posts: 71; Joined: Tue Mar 03, 2009 1:24 pm

by coolgirl26 » Sat Apr 18, 2009 5:13 pm

a business man bought 24 kg of cereal at price x per kg

1/3 of stock got spoiled so business man sold remaining cereal box at 200 per kg

the business man made overall profit= 2x the cost of purchased stock

what was original price per kg= x?

answer is 44 4/9

help me solve this problem i dont get it

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Source: Beat The GMAT — Problem Solving | Sat Apr 18, 2009 5:13 pm

truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Sat Apr 18, 2009 5:38 pm

The man bought 24 grams of cereal at x dollars per gram, so this means that he paid a total of 24 * x dollars for the cereal. Since 1/3 of the 24 grams of cereal got spoiled, the man only had 24*2/3 or 16 grams of the cereal left. Since he sold these 16 grams of cereal at 200 dollars per kg, he mad 200*16= 3200 dollars and this 3200 dollars subtracted to the total amount that the man spent for the cereal (24x) is the profit. We know from the problem that the profit is 2 times the cost of the purchased stock or 2*24x=48x. We can form an equation from this information and find the value of x:

3200-24x=48x
x=44 4/9 dollars per kg.

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