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The retail price of a sweater is $32. If the store can sell the sweater at a 25% discount and still earn a 25% profit on the price it paid the manufacturer for the sweater, how much did the store pay to the manufacturer?

25% discount gives \(\frac{32}{4}\)=8 so price = 32-8 = 24
As shop still earns a profit of 25%, the cost price is 24-24*\(\frac{1}{4}\)=18
Option: C
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Bunuel
The retail price of a sweater is $32. If the store can sell the sweater at a 25% discount and still earn a 25% profit on the price it paid the manufacturer for the sweater, how much did the store pay to the manufacturer?

A. $16
B. $17.20
C. $18
D. $18.60
E. $19.20


Hi,

Those who have answered C as answer, you will have to relook into answer..

Remember ( in such Q)
1) if it's discount, the % will be on the amount/retail price.
2) if it's profit, the amount already contains the profit & so profit will not be on retail price.

Let's see the Q..

Retail price is 32..
Shopkeeper gives a discount of 25% so the price he sells at is \(32*\frac{100-25}{100}=24\)..

Now this has a profit of 25%, so actual price becomes... \(24=\frac{100+25}{100}*x\) where x is actual price.
So x= 24*4/5=19.2

E
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Bunuel
The retail price of a sweater is $32. If the store can sell the sweater at a 25% discount and still earn a 25% profit on the price it paid the manufacturer for the sweater, how much did the store pay to the manufacturer?

A. $16
B. $17.20
C. $18
D. $18.60
E. $19.20

Since the shop owner needs to make a 25% profit, he needs to make 25% of his cost. We can express this in the following equation, in which P = profit and C = cost:

P = 0.25C

Since Profit = Revenue - Cost, and the sweater was discounted 25%, we have the following equation:

(0.75)(32) - C = 0.25C

24 = 1.25C

2400/125 = C

C = 19.2

Answer: E
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Bunuel
The retail price of a sweater is $32. If the store can sell the sweater at a 25% discount and still earn a 25% profit on the price it paid the manufacturer for the sweater, how much did the store pay to the manufacturer?

A. $16
B. $17.20
C. $18
D. $18.60
E. $19.20


Hey,

    • Retail Price or MRP \(= $ 32\)
    • Percent discount \(= 25\)%
      o Hence Selling Price (SP) \(= 32 * ( 1- \frac{1}{4}) = $ 24\)
    • Profit earned \(= 25\)%
      o We can write, \(CP * ( 1 + \frac{1}{4}) = SP = $24\)
      o Hence, \(CP = $ 19.2\)
    • This CP is the amount paid by the store to the manufacturer. Hence the correct answer is Option E.


Thanks,
Saquib
Quant Expert
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