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A trader marked his goods at 20% above the cost price. He sold half

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Re: A trader marked his goods at 20% above the cost price. He sold half [#permalink]
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SiddharthR wrote:
TheNightKing wrote:
A trader marked his goods at 20% above the cost price. He sold half the stock at the marked price, one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the marked price. His total gain is
(a) 2%
(b) 4.5%
(c) 13.5%
(d) 15%
(e) 12%

Hello VeritasKarishma, Bunuel could you please explain the solution to this problem ?

I used the method provided on one the posts which emphasizes the relation between marked up prices and profits -->

(1 + Markup %) (1 - Discount%) = (1 + Profit%)

Using this formula, I got the following --> Profit of 20% for half of the items, Loss of 4 % for a quarter and Loss of 28 % for the other quarter

After this to calculate total gain, I just assumed there are a total of 4 items each at a cost price of 10\$. I split these 4 items into the following.

1) 2 items with a profit of \$2 (20% of Cost Price for each item) -> Total Profit = \$4
2) 1 item at a loss of \$ 0.4 (4% of Cost Price for each item) -> Total Loss = \$ 0.4
3) 1 item at a loss of \$ 2.8 (28% of Cost Price for each item) -> Total Loss = \$ 2.8

When I use the above numbers to calculate percentage, I get ([4 - (0.4 + 3.2)] / 10) * 100 = 0.08 = 8 %

What am i doing wrong here

There are two mistakes one is you have taken \$10 in the denominator which is \$40, and second is although it has not impacted is total is \$3.2 in the numerator.

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A trader marked his goods at 20% above the cost price. He sold half [#permalink]
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Let’s assume Cost price is 100 and total number of items = 4
so marked price 20% above 100 which is 120

total cost price = 100*4=400

now half goods sold at marked price = 2*120=240
quarter sold at 20% discount on marked price = 1*96 =96
remaining sold at 40% discount on market price =1*72=72

total = 240+96+72=408

total gains =408-400=8

8/400*100= 2%

ANSWER:A

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Re: A trader marked his goods at 20% above the cost price. He sold half [#permalink]
gurmukh wrote:
SiddharthR wrote:
TheNightKing wrote:
A trader marked his goods at 20% above the cost price. He sold half the stock at the marked price, one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the marked price. His total gain is
(a) 2%
(b) 4.5%
(c) 13.5%
(d) 15%
(e) 12%

Hello VeritasKarishma, Bunuel could you please explain the solution to this problem ?

I used the method provided on one the posts which emphasizes the relation between marked up prices and profits -->

(1 + Markup %) (1 - Discount%) = (1 + Profit%)

Using this formula, I got the following --> Profit of 20% for half of the items, Loss of 4 % for a quarter and Loss of 28 % for the other quarter

After this to calculate total gain, I just assumed there are a total of 4 items each at a cost price of 10\$. I split these 4 items into the following.

1) 2 items with a profit of \$2 (20% of Cost Price for each item) -> Total Profit = \$4
2) 1 item at a loss of \$ 0.4 (4% of Cost Price for each item) -> Total Loss = \$ 0.4
3) 1 item at a loss of \$ 2.8 (28% of Cost Price for each item) -> Total Loss = \$ 2.8

When I use the above numbers to calculate percentage, I get ([4 - (0.4 + 3.2)] / 10) * 100 = 0.08 = 8 %

What am i doing wrong here

There are two mistakes one is you have taken \$10 in the denominator which is \$40, and second is although it has not impacted is total is \$3.2 in the numerator.

Posted from my mobile device

Oh Lol. Thank you so much for that Guru What a blunder !
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Re: A trader marked his goods at 20% above the cost price. He sold half [#permalink]
The key is to identify easy multipliers.
When you go with 100 as the cost - it boils down to figures of 120, 96 and 72 for the respective marked price, 20% disc and 40% disc.

Now, if you have also assumed 100 as number of stock; then it gets cumbersome and math becomes difficult.

We can use 40 as number of stocks, and it will be very easy to mutiply -

20 * 120 =2400
10* 96 = 960
10* 72 = 720 TOTAL REVENUE - 4080/-
TOTAL COST - 4000/- (40*100)
TOTAL PERCENTAGE PROFIT - 2% (80/4000).
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Re: A trader marked his goods at 20% above the cost price. He sold half [#permalink]
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Re: A trader marked his goods at 20% above the cost price. He sold half [#permalink]
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