A merchant sells an item at a 20% discount, but still makes a gross pr

I have explained the concept below from which we derive the following formula. It makes calculations very simple and you don't need to learn up the formula because it will make sense and stick with you once you go through the explanation:

\(( 1 + \frac{m}{100}) * (1 - \frac{d}{100}) = (1 + \frac{p}{100})\)
where m% is mark up %, d% is discount % and p% is profit %.

Using the formula to solve your question:
If d = 20 and p = 20,
\(( 1 + \frac{m}{100}) * (1 - \frac{20}{100}) = (1 + \frac{20}{100})\)
\(( 1 + \frac{m}{100}) * (\frac{4}{5}) = (\frac{6}{5})\)
m = 50
Therefore, the merchant had marked up by 50% which would have been his profit had he not given the discount.


Let me explain the concept now.
Let us say cost price of an item is $100. I, a merchant, mark it up by 40% and put a tag on it of $140. Now, I have a sale and I offer everything at 10% discount. So something that is marked at $140, will get $14 off and will be sold at $126. The profit I made on the item is $26 (= 126 - 100 (which was my cost price)). This profit is equal to a profit % of 26/100 = 26% (Profit/CP x 100)
Note here that my mark up % was 40%, I gave discount of 10% but my profit is only 26%, not 30%. This is because the 40% mark up was on cost price while when I gave discount, I gave 10% on the marked price (which was way more than cost price). The diagram below will make this clearer.

We can make up a quick formula.
If m% is the mark up %, d% is the discount % and p% is the profit %, then
cost price x ( 1 + m/100) = marked price
marked price x (1 - d/100) = selling price
which means: cost price x ( 1 + m/100) x (1 - d/100) = selling price
We know, cost price x (1 + p/100) = selling price
From the 2 equations above, \(( 1 + \frac{m}{100}) * (1 - \frac{d}{100}) = (1 + \frac{p}{100})\)

In other words, when cost price is increased by m% and then decreased by d%, it is equivalent to increasing the cost price by p%.
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regular price = $100
discounted price = $100 - 20% = $80

c + .2c = 1.2c = 80
c = 66.6

if sold at regular price, profit is 100-66.66 = 33.33

33.33/66.66 = 50% (C)

Let the Market Price of the product is MP.
Let the Original Cost Price of the product is CP.

Selling Price (Discounted Price) = 100%of MP - 20%MP
= 80% of MP. ---------------- (1)

Profit made by selling at discounted price = 20% of CP -------------- (2)

Apply the formula:

Profit = Selling Price - Original Cost Price
=> 20% of CP = 80% of MP - 100% CP
=> MP = 120CP/80 = 3/2 (CP)

Now if Product is sold without any discount, then,

Profit = Selling Price (without discount) - Original Cost Price
= Market Price - Original Cost Price
= MP - CP
= 3/2 CP - CP
= 1/2 CP
= 50% of CP

Thus, Answer should be C.

Nice question.

- Brajesh

the OA is (C)

The "trick" is to find the original cost ---> C

80-Cost = Profit

P/C = 20/100

(80-C)/C = 20/100

80-C = 1/5*C

80 = 1/5*C+C

80 = 6/5*C

400 = 6*C

C = ~67

hence ---> 100-67=33 ---> 33/67 = ~50

S: selling price
C: cost

0.8S - C = 0.2C --> 0.8 S = 1.2 C --> S = 1.5 C
S - C = 1.5 C - C = 0.5 C

ANS: C [50%]

Ans: C

Suppose the cost price as 100.

The managed to sold it with 20% profit. Thus, he sold it for 120.

And 120 was the discounted rate of 20%. 120 is 80% of 150.

So, the marked price was 150, selling at which would incur a good profit of 50%.

Let the selling price = 300

Discount = 20% = 60

Received Amount from customer = 240

240 includes 20% profit

Cost price \(= 240 * \frac{120}{100} = 200\)

If no discount given, then shopkeeper would have earned 300 - 200 = 100 on the item costing 200

His "would be" profit percentage \(= \frac{100}{200} * 100 = 50%\)

Answer = C

Honestly its very easy question provided you pick the right numbers

Lets assume the SP is 120. So offering a 20% discount, the merchant sells at 96 and on this he make a 20% profit. So his cost is 80.

Now of if he sells without the discount then the profit on cost would be 120-80/80 = 50%..

Should be able to do it under 1 min though

Hi All,

This question is perfect for TESTing VALUES, but you have to be very careful about how you do the math. Let's break this into pieces...

A merchant sells an item at a discount and makes a gross profit of 20% on the cost.

Let's TEST VALUES:
Cost = $100
Discount Price = $120
Here we have a 20% profit on the cost...

Regular Price = $X

Now, let's factor in the fact that the sale price was a 20% discount...

$120 = X - (.2)(X)
$120 = .8X
$1200 = 8X
$150 = X

So, the regular price was $150.

We're asked what the profit would have been WITHOUT the discount:
Cost: $100
Regular Price = $150

Profit = (150 - 100)/100 = 50/100 = 50%

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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I am going to tell you an amazing way to do this in matter of 10 seconds. Please have patience with me and see below. Once you grab the concept profit loss and mixtures questions will become your strongest points.

120/100 = 80/100 * x

if you do basic calculations X is 3/2
This means 50% increase. This is the answer


how I did it? See when we say he gave a discount of 20% , it is upon some value be it 100 or 50 or 25 or 78 or 10000 --- > so 20% discount means he sold at 80% of the value? got it? see how.

100-20 / 100 = 0.8,
50-10/50 = 0.8

take any value the ratio will be 8/10
now we can see he clearly made a loss but must have done something that resulted in 20% overall profit. Right? That something is x in the equation.

so that X is your answer when he doesn't give the discount.


In short, no need to take values as left hand common part will be cancelled with right side of equation.


Good Luck

Here is a simple solution:

M.P. x 0.8 = C.P. x 1.2

M.P = (C.P. x 1.2)/ 0.8

M.p. = C.P. x 1.5

Hence 50%

Solution:

Let the MP be 100

=>After a discount of 20% the SP would be 80

This still causes a profit of 20%=>If we have a CP the SP is actually 1.2 CP which is represented by 80 as calculated above.

=>1.2CP =80

=>CP =80/1.2 = 800/12 = 200/3

=>Profit percentage = SP-CP/CP *100

= 100 - 200/3 / (200/3) * 100 (SP is 100 without the discount)

=100/3 * 3/200 *100

= 50% (option c)

Devmitra Sen
GMAT SME
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Let's start by defining by some variables:
(1) Let's say that the item price BEFORE the discount is equal to I
(2) Let's say that the cost is equal to C.

Defining the discounted price:
So first off we are provided that the revenue actually earned is equal to 80% of item I, so (4/5)I.

Determining the Cost:
Next we're provided that at the discount price of (4/5)I a gross profit as a percentange OF COST is equal to 20%, or (1/5). So then we can set-up a ratio as follows:

((4/5)I - C)/C = (1/5), and now when we solve this equation in terms of I we get (2/3)I. So then that means that the cost of the product is (2/3) of the stated price of the product.

Note: Remember to think of % as DIVIDE BY 100, so 20% = 20/100 = 1/5.

Finding the answer:
So now let's translate what the stem wants us to find into an equation. (X/100) times (2/3)I = I - (2/3)I in which (X/100) is equal to "what percent" and profit without a discount is defined on the right hand side of the equation. So when we solve this equation I cancels out and we're left with X = 50, which is our answer.

As KarishmaB very elegantly put it, I am just adding on top of that.
The formula that Karishma wrote can be interpreted as
mark up factor x discount factor = profit factor

We need to find mark up factor (m), and we are given discount and profit as both 20%
when 20% expressed as a discount, this is equivalent a factor of 4/5
Similarly, when 20% expressed as a profit, it is equivalent to a factor of 6/5

So,

m x 4/5 = 6/5
m= 6/4 =3/2 Which is nothing but a 50% increase in the factor of cost price. So mark up is 50% and profit would be 50% without discount,
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