A dealer offers a cash discount of 20%. Further, a customer bargains a

Question

A dealer offers a cash discount of 20%. Further, a customer bargains and receives 20 articles for the price of 15 articles. The dealer still makes a profit of 20%. How much percent above the cost price were his articles marked?

A) 100%
B) 80%
C) 75%
D) 66+2/3%
E) 50%

A) 100%
B) 80%
C) 75%
D) 66+2/3%
E) 50%

IanStewart · Accepted Answer

When you buy 2 things for the price of 1, you get each thing at 1/2 price. Similarly, when you buy 20 things for the price of 15, you get each thing at 15/20 = 3/4 of its normal price.

So in this question, the buyer gets two separate discounts - because he gets 20 for the price of 15, that reduces the overall price to 3/4 of its original value. And the buyer gets a further 20% cash discount, which reduces the price again by 1/5, so to 4/5 of its previous value. So combining the two discounts, the buyer gets each item at (3/4)(4/5) = 3/5 of its original sales price. If  s  is the original sales price, the buyer buys each item for (3/5) s  dollars. We know this is 20% more than what the seller paid for each item, so it is 6/5 of what the seller paid. If the seller paid  p  dollars, then

(3/5)s = (6/5)p
s = 2p

and the sales price is double the purchase price, and the markup is 100%.

You can also solve by just inventing a simple number for the original sales price, though I find this a bit more confusing than the more algebraic solution above. Say the original sales price is $10. We know the seller gives a 20% discount, so the buyer is paying $8 for the 15 items, or $120 in total. But then the seller offers 20 items instead of 15, so the buyer pays 120/20 = $6 per item. The seller still turns a 20% profit, and since $6 is 20% more than $5, the seller must have bought each item for $5. Since the number we chose, $10, for the sale price is 100% bigger than $5, then 100% is the markup.

itzmyzone911 · Answer

Good question...2:11 min

Marked Price (M) = Cost Price (C) + Mark up...(EQN. A)

Selling price = 20% Discount over M = 0.8*M

Given that, a customer bargains and receives 20 articles for the price of 15 articles-->   *a  further loss of 25%  to the dealer  --> BUT a  NET PROFIT of 20%  over cost price (C)

0.75  * 0.8 * M =  1.2 * C

Hence, M/C = 2/1 = 200%

From Eqn. A , (C + Mark up)/C = 200% -->  Mark up / C = 100%

Ans. A

*How to arrive at 25% loss without much ado...%Loss = Goods sold in excess (5) / Goods sold (20). Similarly if the dealer were sly enough to sell 15 for the price of 20, percentage profit = Goods left/Goods sold = 5/15 = 33.3%

Patronus · Answer

Thank you much for the explanation. I normally prefer method 1 too!

But since this discount concept is a bit new, I have two questions:
1) Why is it that when you buy 20 things for the price of 15, you get each thing at 15/20 = 3/4 of its normal price. Why is it not 3/4  "off"  the normal price?
2) Also, why are  s  and  p  different. Should not they be equal?

IanStewart · Answer

You might think of a simpler numerical example first. Say you want to buy 3 apples, and each apple costs $1. That would normally cost you $3 in total. But if the seller gives you an extra apple for free, so you get 4 apples for the price of 3, then you only pay $3/4 = $0.75 per apple. So each apple costs you 3/4 of what it would normally cost, or in other words, you get 1/4 off the price of each apple. Similarly in this question, if we get 20 things for the price of 15, each thing costs 15/20 of what it normally would (so we get a discount of 5/20 = 1/4 = 25% "off" the price of each thing).

When someone is selling something at a markup, or at a profit, they bought it at one price ( p  in my example, sometimes called the 'purchase price'), and they sell it at a higher price ( s  in my example, sometimes called the 'sale price' or 'selling price'). So if someone makes a profit or marks up an item, it must be true that  s  >  p .

Again you might look at a simpler numerical example first - if you buy a television for $100 and sell it for $160, then p = 100 and s = 160, and your percent profit is 60%. The question you posted is a bit confusing, because the seller first marks up the price, then discounts the price, and we need to use the discounted price to work out the profit.

dina98 · Answer

Tried plugging in some numbers:

15 items supposed to sell for $120 originally but 20 were given for this price. 
So the price of each of the 15 items was - $8

there was a 20% discount on the 20 items bought for 120 so 20 items sold at $100. (each item at $5)
Dealer still made a profit of 20% on $5 item so that means the cost to produce each item was $4.

Original markup was $8. And each item was produced with $4. So 100% markup.

vivekximb · Answer

Let the Marked Price for 1 item be 100----For 20 items its 2000 After initial cash disc of 20%, Sale Price of 1 item is 80 and 20 items is 1600 For 20 Items price paid will be 1600; For 15 items it would have been 1200, so by paying 1200 he bought 20 items whose price before cash discount was 2000 The final payment of 1200 still has 20% profit in it, thus Cost Price is 1000 as against Marked Price of 2000 :-D

umg · Answer

Shortest Method Here..

Marked Price = M.P.
Cost Price = C.P.
Selling Price = S.P.
Disc. offered on M.P. = 20%

Bargain Disc. =  \frac{(5*100)}{20}  = 25%

Total Discount on M.P. = -20 - 25 +  \frac{(20 * 25)}{100}  = -45 + 5 = -40% (Successive Percentage Change)

This means that Total Discount Offered by Dealer on M.P. = 40% 
=> S.P. = 0.6 M.P.

Dealer Makes a 20% Profit.
=> S.P. = 1.2 * C.P.

Equating S.P.

=> 0.6 M.P. = 1.2 C.P.
=> M.P. = 2 * C.P.

Therefore, Mark up = 100%

P.S: Formula for Successive Percentage Change => a + b +  \frac{ab}{100} . In this question, a = -20%; b = -25% And, ab = (-20) (-25) = +500

KarishmaB · Answer

For more on this concept, check: https://anaprep.com/arithmetic-markup-discount-profit/

umg · Answer

Thanks for the link but I do have 1 issue in that solution and no its not a technical one; it is an execution-al issue..

I do understand that you have calculated the answer without computing the Second discount (pic attached) but I am not sure whether I would want to do things in such a complex manner at the end. I see a lot of room for error in thinking and I have always found it better to do things  on paper  in a manner as simple as possible because of all the pressure and tension that mounts up during the exam.

Leo8 · Answer

A dealer offers a cash discount of 20%. Further, a customer bargains and receives 20 articles for the price of 15 articles. The dealer still makes a profit of 20%. How much percent above the cost price were his articles marked?

A) 100%
B) 80%
C) 75%
D) 66+2/3%
E) 50%

Cost Price = X
Selling Price = Y
After 1st discount = 0.8Y

to find the 2nd discounted price, we must solve the equation given = 20 * ( 2nd price) = 15 * 0.8y

2nd Discounted price = 12/20 y = 0.6y

Given - Dealer makes 20% profit even on this discounted price

which means 0.6y = 1.2x or y = 2x : which means the selling prices is marked 100% above the cost price - Ans A

Turkish · Answer

Hello Karishma,

I did it in a different way not sure if it is correct

I took 1 articles priced at $100 . 20 articles *100= 2000 now he sold for 20% discount hence 20*80=1600. Further she bough it for the price of 15 articles hence 15*80=1200 this is selling price. It is also told the vendor made 20% profit. We know Selling Price= Cost+Markup, 1200= C +C/5; C= 1000.

From here we know the cost is 1000 and the selling price was 2000. 100%

KarishmaB · Answer

Yes, this is correct. You are just going back and applying the two discounts one by one and then reducing by the profit to get the cost price.

warrior1991 · Answer

Let us take Price of 1 article=x
Price of 20 article=20X (This is our Marked Price)

Now after bargain 20 articles are sold at price of 15 articles i.e 15x

A discount of 20% is also applied finally 
Final S.P= 15x*0.8(20% discount)
Therefore , SP=12 X

Profit earned =20%
CP*1.2=SP
CP=12x/1.2=>10 X

Now it is asked percentage difference between Marked price(20X) and C.P(10X)

You can see this is 100% increase. Therefore A is correct

somyamehta777 · Answer

Discount 1 - 20%
Discount 2 - 20 articles for price of 15 - 25% discount
Let x be SP -> After discount 1 -> 0.8X -> After discount 2 -> 0.8x - 0.8x*(25/100) = 0.6X

Now let CP -> Y 
We know after discounts, we are still making 20% profit, so in terms of y -> 1.2Y

0.6X = 1.2Y
X=2Y = 100% marked up price

Archit3110 · Answer

let cost of each item be 100
so after discount cost of item ; 80
now customer has purchased items worth actual 2000 at the price of 15 articles i.e 15*80 ; 1200
but still dealer has made a profit of 20% ; i.e he has sold at price 100*1.2 ; 120 each so net price of 20 would have been 120*20 ; 2400
% above cost price of articles was ; 2400-1200/1200 ; 100 %
option A

Sambon · Answer

KarishmaB 
This question should be reworded for clarity. What makes us interpret that there were two successive discounts instead of one?
The question says that the "dealer offers a cash discount of 20%. Further, a customer bargains and  receives  20 articles for the  price of 15 articles .

My understanding as I read: A dealer offers a discount of 20% but the customer negotiates further and receives 20 articles for the price of 15 articles, meaning that he negotiated a 25% discount instead of a 20% discount.
If x is the new price of the article, y is the original price, and C is the cost:
 20x=15y  
 x=\frac{3}{4}*y 
 \frac{3}{4}y = \frac{6}{5}C  
 y = \frac{8C}{5}  (the original price was therefore marked up by 60% above the cost if you consider only one discount)

Now I understand that 60% is not a possible answer choice, and we should be reflecting back on the question to see what we did wrong. But nothing in the sentence indicates that there should be two successive discounts. Thoughts?

Kinshook · Answer

Given: A dealer offers a cash discount of 20%. Further, a customer bargains and receives 20 articles for the price of 15 articles. The dealer still makes a profit of 20%.

Asked: How much percent above the cost price were his articles marked?

Let the articles be marked p% above the cost price and cost price be c.

Mark up price = c (1+p%)

After discount price = .8c(1+p%)

Price after bargaining = 15/20 * .8c(1+p%) = 1.2c
1+p% = 1.2/.8 * 20 /15 = 3/2 * 4/3 = 2
p% = 100%

IMO A

GMATGuruNY · Answer

Let the cost price for each article = 10, implying that the total cost for the 20 articles received by the customer = 20*10 = 200

We can PLUG IN THE ANSWERS, which represent the markup.
The dealer makes a profit of 20%.
Implication:
When the correct answer is plugged in, the total revenue for the sale = 200 + (20% of 200) = 200+40 = 240

Note:
The customer receives 20 articles but pays for only 15.

B: 80% markup --> regular selling price = $18 per article
Regular price for 15 articles = 15*18 = 270
Since the customer receives a 20% cash discount, the total revenue for the 15 articles = 270 - (20% of 270) = 270-54 = 216

The total revenue is too small.
Implication:
The required markup must be greater than 80%.

A

ish__02 · Answer

Here is my approach -

Let the cost price be : x 
Selling price : x * y(markup)

CP - 20y 
Final SP : 15*x*y*0.2

Given % profit = 20%

1/5 = 15*x*y*.2 - 20y / 20y

x= 2
ie 100% increase

A dealer offers a cash discount of 20%. Further, a customer bargains a

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A dealer offers a cash discount of 20%. Further, a customer bargains a

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