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A store sells three types of calculators, model A, model B and model C

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A store sells three types of calculators, model A, model B and model C [#permalink]

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New post 08 Jan 2018, 23:53
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A store sells three types of calculators, model A, model B and model C. The selling price of model A is $66, which is 120 percent that of model B, while the selling price of B is p percent of that of C. If the manufacturer sells 2000 calculators, 1/4 of which are model B, and an equal number of A and C models and the total revenue from the sale of calculators is $242,000, what is the value of p?

A. 60
B. 35
C. 25
D. 20
E. 15

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Re: A store sells three types of calculators, model A, model B and model C [#permalink]

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New post 09 Jan 2018, 00:40
1
Hi everyone,

Prices:
A - 66$
B - 66*5/=55$
C - 55*100/p$
Quantity:
A - 2000*1/4=500
B - (2000-500)/2=750
C - 750
Equation:
500*55+750*66+750*55*100/p=242000 | divide both sides by 250
110+198+165*100/p=968
100/p=4
p=25

ANS: C

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Re: A store sells three types of calculators, model A, model B and model C [#permalink]

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New post 09 Jan 2018, 03:42
1
Bunuel wrote:
A store sells three types of calculators, model A, model B and model C. The selling price of model A is $66, which is 120 percent that of model B, while the selling price of B is p percent of that of C. If the manufacturer sells 2000 calculators, 1/4 of which are model B, and an equal number of A and C models and the total revenue from the sale of calculators is $242,000, what is the value of p?

A. 60
B. 35
C. 25
D. 20
E. 15



An easier calculation than the above, using smaller numbers, involves a shortcut using the logic of averages.
This is a Logical approach.

Instead of calculating the total revenue, we'll calculate the average revenue.
As there are 2000 calculators, the average revenue per calculator 242,000/2,000 = $121.
Since 1.2B = 66 then B=55.
Additionally as 2000/4=500 of the calculators are model B then (2000-500)/2 = 750 are model A and C.
Then the ratio A:B:C is 750:500:750 = 3:2:3
So if we take 3 units of A, 2 of B and 3 of C their average is the average revenue per calculator - $121.
3*66 + 2*55 + 3C = 121*8
198 + 110 +3C = 968
3C = 660
C = 220
Therefore B/C = 55/220 = 1/4 = 25%.
(C) is our answer.
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Re: A store sells three types of calculators, model A, model B and model C [#permalink]

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New post 09 Jan 2018, 11:35
Bunuel wrote:
A store sells three types of calculators, model A, model B and model C. The selling price of model A is $66, which is 120 percent that of model B, while the selling price of B is p percent of that of C. If the manufacturer sells 2000 calculators, 1/4 of which are model B, and an equal number of A and C models and the total revenue from the sale of calculators is $242,000, what is the value of p?

A. 60
B. 35
C. 25
D. 20
E. 15


We can also use some approximation:

Price of model A = $66
Price of model B = (100/120)*66 = (5/6)*66 = $55

Average price of all calculators = 242000/2000 = $121

1/4 are model B, 3/8 are model A, 3/8 are model C
The average of A and B would be somewhere around 60.

So now the weighted average of 60 and price of C is 121. Visualising the scale method, the distance between 60 and 121 and distance between 121 and price of C would be in the ratio 3:5. So price of C would be around 220.

The selling price of B is (55/220)*100 = 25% that of selling price of C.

Answer (C)
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Re: A store sells three types of calculators, model A, model B and model C   [#permalink] 09 Jan 2018, 11:35
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