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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 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%
[Reveal] Spoiler: OA

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When you buy 2 things for the price of 1, you get each thing at 1/2 price. Similarly, when you but 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.
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Re: A dealer offers a cash discount of 20%. Further, a customer bargains a [#permalink]

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New post 21 Jun 2015, 22:43
IanStewart wrote:
When you buy 2 things for the price of 1, you get each thing at 1/2 price. Similarly, when you but 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


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?
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New post 21 Jun 2015, 23:21
Patronus wrote:

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?


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).

Patronus wrote:

2) Also, why are s and p different. Should not they be equal?


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.
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A dealer offers a cash discount of 20%. Further, a customer bargains a [#permalink]

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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%

Last edited by itzmyzone911 on 22 Jun 2015, 09:36, edited 1 time in total.

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Re: A dealer offers a cash discount of 20%. Further, a customer bargains a [#permalink]

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New post 22 Jun 2015, 03:46
Thank you once again for clarifying!
I am learning new way to do Quant with your help.

IanStewart wrote:
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).


I tried understanding this using algebra.
E.g.: 20 \(p_1\) = 15 \(p_2\)
4 \(p_1\) = 3 \(p_2\)
\(p_2\) = \(\frac{4}{3}\)\(p_1\)
So, for every $1 I am paying 4/3 after the 2nd case.

I don't understand why isn't this value 3/4 as per your logic.
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Re: A dealer offers a cash discount of 20%. Further, a customer bargains a [#permalink]

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New post 02 Jul 2015, 09:43
Solve it backwords.

Say the dealer cost is 100$, and he sold the items with 20% marginn, thus 120$ it was price.
But for 120$ the customer bought 15 items for the price of 20, we need to find out original price. 120$/15 is the price per piece we need to find out how much is 20. 120/15=8*20=160.
Plus additional 20% cash discount,so the customer only paid 80%. so original price was 160/80*100=200$. So the dealer has 100% markup.

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A dealer offers a cash discount of 20%. Further, a customer bargains a [#permalink]

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New post 12 Dec 2015, 17:35
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.

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Re: A dealer offers a cash discount of 20%. Further, a customer bargains a [#permalink]

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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.


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

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Re: A dealer offers a cash discount of 20%. Further, a customer bargains a [#permalink]

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New post 09 Sep 2016, 03:14
Patronus wrote:
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%

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
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Re: A dealer offers a cash discount of 20%. Further, a customer bargains a [#permalink]

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New post 09 Sep 2016, 04:53
Patronus wrote:
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%


For more on this concept, check: http://www.veritasprep.com/blog/2014/09 ... questions/
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Re: A dealer offers a cash discount of 20%. Further, a customer bargains a [#permalink]

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New post 09 Sep 2016, 05:40
VeritasPrepKarishma wrote:
Patronus wrote:
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%


For more on this concept, check: http://www.veritasprep.com/blog/2014/09 ... questions/

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.
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New post 28 Dec 2017, 14:32
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?

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
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A dealer offers a cash discount of 20%. Further, a customer bargains a [#permalink]

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New post 28 Dec 2017, 15:46
VeritasPrepKarishma wrote:
Patronus wrote:
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%


For more on this concept, check: http://www.veritasprep.com/blog/2014/09 ... questions/


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%

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Re: A dealer offers a cash discount of 20%. Further, a customer bargains a [#permalink]

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Turkish wrote:
VeritasPrepKarishma wrote:
Patronus wrote:
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%


For more on this concept, check: http://www.veritasprep.com/blog/2014/09 ... questions/


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%


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.
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Re: A dealer offers a cash discount of 20%. Further, a customer bargains a [#permalink]

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New post 11 Jan 2018, 14:00
not sure if this logic makes sense:
Let's say the original selling price of item was $100.
20% discount: $100 - $20 = $80
20 for the price of 15 = 25% discount: $80 - 20 = $60
profit margin is still 20% of $60 = $12
$60-$12 = $48 cost of item = approx. 100% markup

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