A shoe manufacturer started offering a standard 25% discount on the

Question

A shoe manufacturer started offering a standard 25% discount on the list price of a pair of shoes. However, a large retailer requested that in addition to the standard discount, they should additionally get 25 free pairs of shoes for every 100 pairs they purchase. The manufacturer calculated that even in this case, he would still make 20% profit on the cost. If the cost price per pair of shoes is $c, then what is the list price of the pair of shoes in terms of c ?

A. 2c
B. 3/2*c
C. 4/3*c
D. 5/4*c
E. 6/5*c

Bunuel · Accepted Answer

Official Solution:

A shoe manufacturer started offering a standard 25% discount on the list price of a pair of shoes. However, a large retailer requested that in addition to the standard discount, they should additionally receive 25 free pairs of shoes for every 100 pairs they purchase. The manufacturer calculated that even in this case, he would still make a 20% profit on the cost. If the cost price per pair of shoes is  $c , then what is the list price of the pair of shoes in terms of  c ?

A.  2c 
B.  \frac{3}{2}c 
C.  \frac{4}{3}c 
D.  \frac{5}{4}c 
E.  \frac{6}{5}c

Observe that the manufacturer essentially offers the retailer 125 pairs of shoes at the list price of 75 pairs — the price of 100 pairs after the 25% discount equals the list price of 75 pairs, and the retailer receives an additional 25 pairs as a gift. The cost price of 125 pairs of shoes is  $125c . Given that the manufacturer still maintains a 20% profit margin, the selling price becomes  $125c *s 1.2 = $150c .

Therefore, we deduce that the list price of 75 pairs equals  $150c , making the list price of one pair equal to  $2c .

Answer: A

Dhruvdaddy1 · Answer

Hey!
My answer is ( A ).

Let the listed price be 's'
Now, A.T.Q, the buyer purchased 100 shoes at a 25% discounted cost, and got 25 free.
So, 3/4*S*100 is the amount he/she payed for 125 shoes.

Now, for the cost price, 'c'.
125 shoes would have cost the shopkeeper 125*c.

Yet, he made a 20% gain.

So, simply putting it in the form of a profit percent equation, we get, (3/4*S - c)/c = 1/5
Which gives, S as '2c'.

Best of luck!
Dhruv

Believe in yourself, you can do it!

gmatophobia · Answer

General discount = 25%

Volume discount

25 shoes free per 100 per pair of shoes.

Inference: So the retailer pays only for 100 pair of shoes.

% Discount =  \frac{25}{125}*100  = 20%

Also, its given that at the end of transaction the shoe manufacturer makes a profit of 20%

Its given that the cost price of per pair of shoes is $c

Let the list price of the pair of shoes be $L

Cost Price to the the  retailer   = $L * general discount * volume discount =  c * (1-\frac{20}{100})*(1-\frac{25}{100})  =  \frac{3L}{5 }

This cost is equal to 20% profit on the cost price to the manufacturer

So,

\frac{120}{100} * c = \frac{3L}{5}

L = 2c

Option A

ABHISEKGMAT123 · Answer

Discount: 25% =1/4
Discount: 25 articles free on each 100 articles---25/125=1/5
Overall profit to be made:20%=1/5
CP SP MP/LP
.....3 4
.....4 5
----------------
.....3 5 Overall effective discount
5 6
----------------
5 6 10
If CP is 5 MP/LP has to be 10
CP=c
MP=2c

Adarsh_24 · Answer

Can we say list price of each shoe first reduced by 3/4 then by 4/5( since 125 shoes for price of 100)
So 6c/5 = 3/5 * list price
List price = 2c

pavanhra · Answer

Let's take for example the List price is 400. on this 25% discount is offered.

400 - 25%(400) = 300 and out of this 25/125 is given as free as quantity discount i.e again 20% discount.

300 - 300*20% = 240, even selling at 240 gives the profit of 20% on cost c i.e

240 = 1.2c, so cost is 200. Now actual question asked here is what time the cost price is list price. cost * 2 = 400 (list price) L = 2C is the answer.

pappal · Answer

cost of one pair=$c
cost of 125 pairs=125c
let list price be L, considering discount of 25%, selling price of one pair=L(1-1/4)=3L/4
total selling price=100*3L/4
selling price =1.2 of cost price 
i.e. 100*3L/4=1.2*125c
L=2c
A

ariyanak · Answer

I solved this by plugging in 100 for the value of the list price.

Let. list price by $100.
So selling price per pair is $75.

at the price of 100 pairs (after 25% discount), the retailer is getting 125 pairs.

So, what's the average price with the free offer plus the 25% discount?

(100*75)/125 = 60 -> this is is the average price.

Given that:
1.2c = 60
c = 50

Going back to l = 100, i see that l = 2c. Hence, A.

Note: I am not the best at deriving algebraic relationships from such word problems. It's a hit or miss. Hence, this approach works for me.

A shoe manufacturer started offering a standard 25% discount on the

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