A wholesaler bought 1,200 radios for $18 each. The wholesaler sold 60

Responding to a pm:

Yes, you can use weighted average here. You want to find the average selling price.
60% of radios were sold at $30 and 40% at $15.
Average selling price = (30*0.6 + 15*0.4)/1 = 24
Average cost price = $18

Average profit = $6
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FACTOR, FACTOR, FACTOR! Fractorization is your best friend
(Do NOT attempt to solve equation, especially any multiplication until all the factorization is completed.)

Total Cost: 1200*18

Sales1: 1200*(3/5)*30 = 1200*18
Sales2: 1200*(2/5)*15 = 1200*6

Ave profit = (Sales1 + Sales2 - Cost) / 1200
= ( (1200*18)+(1200*6)-(1200*18) ) / 1200
= (1200*6)/1200
= 6

The approach shows many details, but in reality all you need is the first line:
"( (1200*18)+(1200*6)-(1200*18) ) / 1200", which should give you '6' right away after you cross them out.

The only arithmetics I had to do were "3/5 * 30 = 18" and "2/5 * 15 = 6"
Do simple arithmetic as you read the question! 18 and 6 were already written on my scratch paper by the time I read the word, "average" in the last sentense
1200 was never even involved
The whole process should not take more than 30 sec.

Hi guys,

For me E

mean price=(720*30+480*15)/1200=24

mean profit=24-18=$6

OA?

Cheers

A wholesaler bought 1,200 radios for $18 each. The wholesaler sold 60 percent of the radios for $30 each and the rest for $15 each. What was the wholesaler’s average (arithmetic mean) profit per radio?

A. $2
B. $3
C. $4
D. $5
E. $6

This is an easy question but I wasnt able to complete it under 2 mins. Is there a shortcut? Thanks![/quote]

TOTAL SALE PRICE - TOTAL COST / NO OF RADIOS SOLD = AVERAGE PROFIT /RADIO

TOTAL COST = 21,600, TOTAL SALE PRICE = 720*30+480*15 = 21600+7200 = 28800

28800-21600 / 1200 = 7200/1200 = 6

E is the answer

Key to solve this question:
- Do not multiply 1,200 with the list price. It will make much longer to solve the problem.
- Try to set up basic equation to see the best possible way to solve the problem.

Profit = Revenue - Cost
Average Profit = (Revenue - Cost) / 1,200 ---------- (1)

Cost = 18 x 1,200 ---------- (2)

Revenue = (30 x 1,200 x 60%) + (15 x 1,200 x 40%) = 1,200 [(30 x 0.6) + (15 x 0.4)]
= 1,200(18 + 6) ---------- (3)

(3) - (2); Revenue - Cost = Profit = 1,200 [18+6] - (1,200 x 18) = 1,200x6 ---------- (4)

Put (4) in (1);
Average Profit = 1,200 x 6 / 1,200 = $6 per radio.

The answer is E.

Thanks karishma,
I was able to identify weighted average concept here,but was unable to proceed.

Using scale method

15$----4-----Average S.P-----6-----30$

W1:W2 = 3:2

Average S.P = 15 + (3/5 X 15) = 24
Average profit = S.P - C.P = 24 - 18 = 6

I think an easy way to answer this problem is to scale it down.
1,200 @ $18
60% @ $30
40% @ $15 Right?

It doesn't matter what number you base your percent on as long as it is a counting number.

So instead of doing the calculations based on 1,200 radios, base the problem on 10 radios.

Purchase Price
10 @ $18 = $180

Sale Price
6 + 4 = 10
6 @ $30 = $180
4 @ $15 = $60
$180 + $60 = $240

Sale Price - Purchase Price = Profit
$240 - $180 = $60

And because we based this problem on 10 radios to find the price per unit we divide $60 by 10

$60 / 10 = $6

|<---------- 6(60%) ------------------->|<-----4(40%)-->|
---------------------------------------------------------------------
15 30


SO the avg will be towards 30 . Exactly 6/10 th of the line segment of 15 units
(6*15)/10 = 9

So avg is 9+15 = 24 i.e $24 per radio. Profit = SP-CP = 24-18 = $6

((0.6.1200*30+0.4*1200*15)-18*1200)/1200=(18*1200+6*1200-18*1200)/1200=6
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60% for a profit of 12
40% for a loss of -3

Ratio is 3:2 between both
Now then, 12(3)-3(2)=30
So average 30/5=6

Hence answer is (E)
Cheers
J

VeritasPrepKarishma

I approached this question using weighted average only, but a little variation.

Since we need to find profit/radio.

C1 = \(12 (30-18)\)
C2 =\(-3 (15 - 18)\)

w1 =\(.6\)
w2 = \(.4\)

\(Cavg\) =\((12*.6 + (-3) * .4 ) / .6+.4\)

\(Cavg = 6\)

Please let me know if it is alright.
Thank you

Yes, you are calculating the weighted average of the profit - that's fine.
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why do we divide by 1 to get the $24?

60% of 1,200 is 0.6 x 1,200 = 720. If these 720 radios are sold for $30 each, they will generate a profit of 720 x (30 - 18) = 720 x 12 = $8,640.

The rest of 1,200 - 720 = 480 radios are sold for $15 each, but they will generate a loss of 480 x (18 - 15) = 480 x 3 = $1,440.

Therefore, the total net profit is 8,640 - 1,440 = $7,200, and thus the average profit per radio is 7,200/1,200 = $6.

Answer: E
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60% or 3/5 of the radios were sold at $30 meaning 40% or 2/5 were sold at $15

radios sold at $30 would be a $12 profit and radios sold at $15 would be a -$3 dollar profit or loss.

12+12+12-3-3

=30/5

=$6 average profit

answer E

Given: 1,200 radios

60% sold for $30 each = \(0.6 * 30\)
40$ sold for $15 each = \(0.4 * 15\)

\((0.6 * 30) + (0.4 * 15) = 24\)

\(24 - 18 = $6 profit\)

Answer is E.
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Hi,

I've solve it with the concept of weighted averages.

Cost price per radio is 18$
60% are sold for 30$ resulting in a 12$ profit per radio
40% are sold for 15$ resulting in a 3$ loss per radio

3/5*12$= 36/5
(2/5)*-3$= -6/5
(36/5)-6/5=30/5=6$
Answer E

\(\frac{ (720*30 + 480*15)-1200*18}{1200}\)

\(= \frac{(216000 + 7200) - 216000}{1200}\)

\(= 6\), Answer will be (E)
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