A customer came to a shop and asked manger to give 20% discount on lis

Question

A customer came to a shop and asked manger to give 20% discount on listed price of a pen.Moreover , for every 10 pens purchased he wanted 2 pens free of cost. The manager agreed to the customer's demand because he could still make a profit of 20% on cost price. If the cost price of a pen is x, what was the listed price?

A)1.75x
B)1.8x
C)1.9x
D)2x
E)2.5x

A)1.75x
B)1.8x
C)1.9x
D)2x
E)2.5x

Archit3110 · Accepted Answer

let value of pen = p
so @ 20% discount = 0.8p
and for 10 pens value would be 0.8p*10 = 8p
since customer is getting 12 pens so price per pen = 8p/12 
now the cost price is 20 % profit or say 1.2 x
8p/12= 1.2x
p= 1.8x
IMO B

Rakesh1987 · Answer

Let the selling price be s.
  The selling price of 10 pens even after discounting by 20%=cost of 12 pens and profit of 20%  
=>10*0.8s=1.2*12x
=>s= \frac{14.4x}{8}  = 1.8x.

Please hit +1 Kudos if you liked the explanation.

IanStewart · Answer

Say the listed price is "p". The customer gets a 20% discount, so each pen costs 0.8p. But the customer is also getting 20% more pens than he is paying for (he gets 2 free when he buys 10). So he is really paying 0.8p for 1.2 pens (20% more than 1), and the cost per pen to him is 0.8p/1.2 = 2p/3.

Now we know this is still 20% greater than the cost of each pen to the seller. Let's call that cost price "c". Then we know the discounted price is 1.2 times c, or 6/5 of c, so we have

2p/3 = 6c/5
p = (3/2)(6c/5)
p = 18c/10 = 1.8c

Fdambro294 · Answer

Let the Original List Price = LP

(Discount 1) 20% Discount on LP

20% Discount ----> Decrease by 1/5 ------> same as 4/5 of LP

(4/5) * LP

(Discount 2) for the Same Price of 10 pens, he wants 2 pens free

Assume each Pen has a $List Price = $24

Original Sales Price BEFORE Discount -----> (10 pens) * ($24 per pen) = $240 Revenue

New Sales Price AFTER Discount ------> (12 pens) * (X per pen) = Same $240 Revenue

the New Sales Price per pen = ($240) / (12) = $20 per pen

Discount Given per pen = ($20 - $24) / ($24) = - (4/24) = -(1/6) Discount

A Discount of -(1/6) -----> (5/6) of the List Price

Multiply the Successive Discounts to get the Final Price the vendor sold the product for:

(5/6) * (4/5) * (LP) = (2/3) * (LP) = Sales Price

(3rd) He was still able to make a 20% Profit Percentage on the Discounted Sales Price, given the Cost Price (CP) = X

Sales Price = CP + (P%) * (CP)

(2/3) * (LP) = X + (1/5)*(X)

(2/3)LP = (6/5)X

LP = (3/2) * (6/5) * X

LP = (18/10) * X

LP = 1.8X

-B-

The Listed Price = 1.8X

Emdad · Answer

Let, the listed price is 100p
On 20% discount it is, 80p

Price of 10 pen is 800p
Actually it is price of 12 because 2 pen is free with 10 pen.

So per pen price  \frac{800p}{12}=\frac{200p}{3} 
In this price he also have 20% profit. 
So,  \frac{200p}{3}=120x
=> p=1.8x

Answer is B

aniruddhawarang29 · Answer

My approach was lengthy I feel.

I assumed LP = 100.
So initial SP = 80.
So SP initial for 10 pens = 800.

On noticing customer is getting per pen for \frac{800}{12} = \frac{200}{3}.

CP * \frac{120}{100} = \frac{200}{3}

We get CP as 1000/18.

Now substitute this 1000/18 in options and you should get LP as 100 because that is what was assumed initially.

For option B 1.8(x) =  
We will get LP as 100.

itsprateek95 · Answer

Discount1 multiplying factor on LP= 8/10
Discount2 multiplying factor on LP= 10/12
Profit multiplying factor on CP= 12/10

Therefore, equating SP....
Listed Price * (8/10) * (10/12) = x * (12/10)

LP = 1.8x

bumpbot · Answer

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A customer came to a shop and asked manger to give 20% discount on lis

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