In a shop, the marked price of an article is worked out in s

Question

In a shop, the marked price of an article is worked out in such a way that it generates a profit of $33\frac{1}{3}%$. What should be the discount percent allowed on the marked price during a sale, so that the final profit made is 20%?

A. $13\frac{1}{3}%$

B. $12\frac{1}{2}%$

C. 10%

D. $8\frac{1}{2}%$

E. $6\frac{2}{3}%$

A.  13\frac{1}{3}\%

B.  12\frac{1}{2}\%

C. 10%

D.  8\frac{1}{2}\%

E.  6\frac{2}{3}\%

KarishmaB · Accepted Answer

Let me explain the concept with easier values.
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.

Attachment:

Ques.jpg [ 13.44 KiB | Viewed 20267 times ]

Now, if I go back to your question, let us say the cost price of the item was $100. It was marked up to $133.33 (to generate a profit of 33.33%) but the actual profit received was only 20% i.e. the item was sold at $120. Then, discount % = (133.33 - 120)/133.33 x 100 = 10%

Same thing can be done using multipliers (as shrouded1 has done above)
When cost price, c, increases by 33.33%, it becomes c + 33.33c/100 = c(1 + 33.33/100) = c4/3. This is the marked price (also called tag price)
Profit = 20% so selling price must have been c + 20c/100 = c6/5
Discount = 4c/3 - 6c/5 = 2c/15
Discount is always given on the marked price. Discount % = (2c/15)/(4c/3) x 100 = 10%

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, $( 1 + \frac{m}{100}) * (1 - \frac{d}{100}) = (1 + \frac{p}{100})$

If I am to use this formula in your question,
$(1 + \frac{33.33}{100})(1 - \frac{d}{100}) = (1 + \frac{20}{100})$
$\frac{4}{3}x (1 - \frac{d}{100}) = \frac{6}{5}$
d = 10

vitamingmat · Answer

lets consider the price of an article is : Rs.100... market it for 133.33 so that u get a profit of 13.33 Rs... So now the price of an article is : Rs.133.33
To get profit of 20% of an article ...i.e., 120 is the selling price.. so that you get a profit of 20% on the Rs.100 article...

So you allowed a discount of 133.33 -120.00 = 13.33 on a market price of an article.

for Rs. 133.33 given discount is : 13.33
for 100 what is the discount price???

13.33*100/133.33 = 10%

shrouded1 · Answer

Lets say the costr price is x.
Original marked price is (4/3)x for 33.33% profit
New marked price for 20% profit is 1.2x
So the discount = (4/3)x-(1.2)x=(4/3)x-(6/5)x=(2/15)x
Discount as a percentage =  \frac{2/15 x}{4/3 x} * 100=10%

AtifS · Answer

Wow! You explained the concept thoroughly and the way that a newbie can understand it very well. Kudos +1 for such a detailed explanation

. Writing the math formulas in a mathematical format will be great for making it visually clear (loved the diagram method).

KarishmaB · Answer

There you go Atif... and yes, I would prefer that one think of the diagram while solving a discount problem rather than the formula. If the concept is clear, no matter how they word the question, it will never be a problem.

jlgdr · Answer

This one's pretty straightforward.

Let's say the cost is 60 and the original price is 80. Now then we have a projected profit of 33%. If we would like to make only 20% we would have to sell at 72$. Therefore the discount is 8/80=10%.

Answer is thus C.
Hope its clear

Cheers!
J

rhine29388 · Answer

lets consider the cost price of an article as $60 (take a number whose 33.33% can be calculated easily)
so marked price = 1.3333*60 = 80
profit to be earned = 20%
final selling price = 1.2*60 = 72
therefore discount to be given = 8/80 = 10%
answer - C

ShashankDave · Answer

Quick way to solve this one..let the price be 1..

\frac{4}{3}*x = \frac{6}{5}

Solving gives
 x = 0.9

Thus discount = 10%
(C)

puneetb · Answer

It would be correct to write that the profit as % instead of absolute number. It confuses despite this being a straightforward problem.

akbindia · Answer

Absolutely. The missing % sign is hugely confusing. Not only that, option (C) should be mentioned as 10 rather than 10%. These confusing tactics are unwarranted and never deployed by GMAC.

Posted from my mobile device

Harsh9676 · Answer

IMO C

Let the cost price be 100 , so the mark up price would be 133.33

Now the overall profit to be 20% on cost price, the Mark price should be 120

So the original Mark up price of 133.33 should be reduced by 13.33 to make it 120.

The percent change is 10% (10% of 133.33 is 13.33)

YB114 · Answer

we know when CP(Cost Price) increases with some percentage then we called it Marked price thus , let say that percentage is M
thus CP(1 + M%) = MP

Given that on this MP (marked Price) one can earn profit of 33.34% thus it means CP increased by 33.34% 
CP(1 + 33.34%) = MP 
1.3334 CP = MP

During sale , some discount has been offered thus profit earn on that SP (sellinf price) after discount is 20%

MP(1 - D%) = SP

we know profit earn on CP thus we can say SP =1.2CP and as we know  MP=1.3334 CP

1.3334CP(1 - D%) = 1.2SP

0.1334CP= 1.3334CPD%
D%= 0.1334/1.3334 = 0.10

D/100 = 0.10
D= 10%

Ankur17000 · Answer

Choose the cost price as 150 as 33.3% of this is 50, so the markup would be 200.

So for 20% profit, we would need 120% of 150, which would be 180.

200 * X/100 = 180

X = 90, so the discount needs to be 10%

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