what is the ans and why?

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Inspired: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Sun May 24, 2009 7:27 am; Location: Glasgow

what is the ans and why?

by Inspired » Tue Jan 19, 2010 1:51 am

A salesman sells two equally priced brands of ice cream, for which he receives a sales commission of 5 percent on one brand and 7 percent on the other. If the salesman sold a total of $10,000 in ice cream and collected $660 in commissions, what fractional part of the total ice cream sold did he sell at the lower commission rate?

7/8 4/5 1/2 1/5 1/8

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Source: Beat The GMAT — Problem Solving | Tue Jan 19, 2010 1:51 am

ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pm; Location: Arabian Sea; Thanked: 125 times; Followed by:2 members

by ajith » Tue Jan 19, 2010 3:13 am

Inspired wrote:A salesman sells two equally priced brands of ice cream, for which he receives a sales commission of 5 percent on one brand and 7 percent on the other. If the salesman sold a total of $10,000 in ice cream and collected $660 in commissions, what fractional part of the total ice cream sold did he sell at the lower commission rate?

7/8 4/5 1/2 1/5 1/8

The actual margin made by the salesman = 660/10000 = 6.6%

that is clearly 0.2*5 + 0.8*7 hence he was selling 20% at lower rates that is 1/5

a more scientific method would be

if he sold fraction x in lower margins, he would have sold fraction (1-x) in higher margins

now x*5+(1-x)*7 = 6.6

=> 7-2x = 6.6
2x = 0.4 and x =0.2 that is 1/5

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