A salesman sells two equally priced brands of ice cream, for which he

Question

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?

(A) 7/8

(B) 4/5

(C) 1/2

(D) 1/5

(E) 1/8

(A) 7/8

(B) 4/5

(C) 1/2

(D) 1/5

(E) 1/8

medic19 · Answer

At first it may have been tempting to construct a table (which I tried and spent 30-45secs) and/or an algebraic equation. Whilst these methods would have demonstrated a clarity of thought attributed only to a high-level accountant, it is in the end easier to use the logic of weighted averages. A commission of USD660 is an effective yield of 6.6% from USD10,000. The average between 5% and 7% is 6%; it therefore appears that we sold "a bit" more on the 7% side. We are left with choices D and E, time is running out - oh no you won't get into Darden! So you go with D just because it seems a more sensible option - the difference between the two is not that big - and you may be right. If you draw out a line of with 5 and 7 at both ends and 6 in the middle, as well as 6.6 closer to 7 you will see that the distance between 5 and 6.6 is 1.6 and the distance between 6.6 and 7 is 0.4 - so that gives us a ratio of the two distances of 4:1 (which can be represented as 4/5 for the one side and 1/5 for the other). Since we know that 7% contributed a bit more to the whole sales mix you know that it contributed 4/5 to the whole mix and therefore 1/5 was contributed by 5%.

It's still early though and I might be wrong.

It's still early though and I might be wrong.

shuvodip04 · Answer

Let the total amount of ice cream sold for the 5% brand be x and that for 7% brand be y.

So we can form two equations from the given conditions:-

x+y = 10000 ....i) and

0.05x + 0.07y = 660
=> 5x + 7y = 66000 .....ii)

Question asks for the fraction of ice cream sold at a lower commission 
So we need to find the value of x as fraction of 10000

Solving i) and ii) we get x = 2000

So the fraction of ice cream sold at lower rate = 2000/10000 = 1/5 Hence (D)

Archit3110 · Answer

x+y= 10,000
.05x+.07y=660
5x+7y=660*100
solve for x
we get
x=2*10^3
so fraction of ice cream sold of low commission ; 2*10^3/10^4 ; 1/5
IMO D

adityasuresh · Answer

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?

(A) 7/8

(B) 4/5

(C) 1/2

(D) 1/5

(E) 1/8

We could use alligation 
Overall commission % = 660/10000* 100 = 6.6%
Brand 1 commission = 5%
Brand 2 commission = 7%

5%(lower commission) : 7%(higher commission)
 \ /
 \ /
 6.6%
 / \
 0.4: 1.6
lower commission = 1/5
 D

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A salesman sells two equally priced brands of ice cream, for which he

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A salesman sells two equally priced brands of ice cream, for which he

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