M40-97

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 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. $\frac{6}{5}c$

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

Bunuel · 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. $\frac{6}{5}c$

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 * 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

tanishqgirotra · Answer

For reference, whenever something as free is provided, to calculate that in terms of disount, we use the formula:

free stuff / free stuff + actual quantity * 100, like in this case, manufacture is giving 25 pair of shoes with every 100 shoes so discount is 25/125*100 = 20%

Rahul885 · Answer

Hi Bunuel,

Am I wrong when I say the discount offered is 25% and then 20% on that. 
By successive % = 25+20+(25*20/100) = net 50%.
Then SP=MP/2
Also since 20% profit. SP=6/5 of CP
So 6c/5=m/2
Hence m=12c/5 ?

Bunuel · Answer

25% and 20% does not give an overall 50%.

100 - 25% of 100 = 75
75 - 20% of 75 = 60.

AbhiS101 · Answer

There is mistake in calculating the second discount

Let the price of one shoe be x & the total price of 125 shoes be 125x

Total price of 100 shoes be 100x

Here, 125 shoes are sold at cost of 100 shoes

(125x-100x)/125, i believe you are keeping denominatior as 100

= 20%

Basically if a vendor is giving 1Kg free grapes with a purchase of 1 kg grapes then he is offering 50% discount.

Posted from my mobile device

AbhiS101 · Answer

Let's solve it with a basic approach 
Profit= Total Sales - Total cost...eqn 1

Let the cost price of one shoe be C & selling price of one shoe be S

Here total sales = 100*S*discount(0.75)
75S

Cost price= 100*c + 25 free shoes
= 125C

Profit= 0.2*C*125

Put these in eqn 1

25C = 75S - 125C
75S = 150C

S = 2C

Posted from my mobile device

Nipunh · Answer

I did not quite understand the solution. we are told:
– cost per pair = c
– standard 25% discount on list price
– retailer also gets 25 free pairs for every 100 paid pairs
– even with this, the manufacturer earns 20% profit on cost

let list price per pair be x

after 25% discount, price paid per pair = 0.75x
retailer pays for 100 pairs but receives 125 pairs (100 + 25 free)
so revenue to manufacturer = 100 × 0.75x = 75x
number of shoes given = 125
so total cost to manufacturer = 125 × c
total profit = revenue − cost = 75x − 125c
but we are told this is 20% profit on cost → profit = 0.2 × 125c = 25c

set up equation:
75x − 125c = 25c
75x = 150c
x = 2c

answer: 2c
correct option is 2c

MegB07 · Answer

Hi,

Please tell if this approach is correct:

Total revenue per pair = 100 x 0.75L/125 = 0.6L
Total cost = C(1 + 20/100) = 1.2C

Selling Price (List price) = Cost price + profit
0.6L = 1.2L

L = 2C

Goldenfuture · Answer

I made a mistake here for doinng successive % change. And if someone else has done this & wondering why this went wrong - the point is you cannot mix price discount to quantity discount. Hard learnings.

M40-97

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