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

Question

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%

sabeer28 · Answer

Let’s assume ; 
Cost price = 100
CP (cost price ) goods with marked price = 120
Sold 1/2 in marked price = 120
And 1/4 with 20% discount = 103.33
Rest with 40 % discount = 86.66
Gain = (120+103.33+86.66)-100/100 
Ans ~ 2., option (A)

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SiddharthR · Answer

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 ( / 10) * 100 = 0.08 = 8 % What am i doing wrong here

gurmukh · Answer

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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kawal27 · Answer

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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avin2788 · Answer

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).

Abinash34 · Answer

Let CP is each stock is 100X, then MP is 120X. Let total stock is M.
Total CP is 100XM, Total MP is 120XM
ATQ,
M/2 sold at MP= 120X * M/2 --(1)
M/4 sold at 20% discount on MP= 96X * M/4 (120X-20% of 120X)--(2)
Another M/4 sold at 40% discount on MP = 72X * M/4(120X-40% of 120X)--(3)

Total price after discount = Eqn: (1)+(2)+(3) i.e 102XM
Profit is SP-CP= 102XM -100XM= 2XM. 
Ans. (A)

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

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

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