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what is the ans and why?

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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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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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by Inspired » Tue Jan 19, 2010 3:31 am
thank you..
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