A bookseller sold 4 rare books for $100 each. He made a profit of 25%

Question

A bookseller sold 4 rare books for $100 each. He made a profit of 25% of his cost on the sale of 2 of them, but lost 20% of his cost on the sale of the other 2. What was his profit or loss, in dollars, on the sale of all 4 books?

(A) Profit of $40

(B) Profit of $20

(C) Profit of $10

(D) Loss of $5

(E) Loss of $10

YB10 · Accepted Answer

For 2 
Cost(1.25)=100
Cost=80

For other 2
Cost(0.8)=100
Cost=125

Total sales = 400- (2*80+2*125)
= -10 (E)

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RenB · Answer

Hi. I got a profit of appx 10$ for this one. Could you please check the OA and update if required?

HarshaBujji · Answer

SP = 100, So CP for first 2 items is:

SP = (Profit%)CP 
So CP = 80 , Profit on 2 books =40

Similarly , CP for next 2 items is:

SP = (Loss%)CP 
CP = 125, Loss on 2 items = 50

Overall it's a loss of 10.

KarishmaB · Answer

If selling price is 100 and profit is 25%, it means the cost price is 100*4/5 = 80. 
Hence profit on two books is $20*2 = $40

If selling price is 100 and loss is 20%, it means the cost price is 100*5/4 = 125. 
Hence loss on two books is $25*2 = $50

Overall there is a loss $50 - $40 = $10

Answer (E)

Percentages Concept Video:  https://youtu.be/HxnsYI1Rws8

justwannastudy · Answer

KarishmaB,

Why can we not use the weighted average technique, similar to the below camera problem? I quickly found +2.5% gain when using alligation, but I'm assuming the weights are wrong?

-20%------------+2.5%---------+25%

"  A photography dealer ordered 60 Model X cameras to be sold for $250 each, which represents a 20 percent markup over the dealer’s initial cost for each camera. Of the cameras ordered, 6 were never sold and were returned to the manufacturer for a refund of 50 percent of the dealer's initial cost. What was the dealer's approximate profit or loss as a percent of the dealer’s initial cost for the 60 cameras? "

RockTale · Answer

You got profit because you chose $100 as CP. It is SP instead.

iamjayysingh · Answer

no way this question is 705 level

GMATinsight · Answer

1.25x = 100
i.e. x = 80

so cost of two books is $80 each

for other books on which he lost 20%

0.80 y = 100
i.e. y = 125

so cost of other two books is $125 each

Total Cost = 80+80+125+125 = 410
Revenue = 400

Loss = 410 - 400 = $10

Answer:Option E

Krish13tss · Answer

Answer: E — Loss of $10.  The entire question is a "% of  what " trap — profit/loss is on  cost , but the $100 is the  selling price . Your documented wrong-base pattern, dead center. Never take the percent off $100.
 The two winners (25% profit on cost): 
 Selling price = cost + 25% of cost = 1.25 × cost. So:

1.25 × cost = 100 → cost = 100/1.25 = 80 each
Two books: cost 160, sold for 200 → profit +40

The two losers (20% loss on cost): 
 Selling price = cost − 20% of cost = 0.80 × cost. So:

0.80 × cost = 100 → cost = 100/0.80 = 125 each
Two books: cost 250, sold for 200 → loss −50

Combine:

Total revenue = 400
Total cost = 160 + 250 = 410
400 − 410 = −10 → Loss of $10

The trap answer is C ($10 profit).  You get it by taking the percentages off the $100 selling price: 25% of 100 = $25 profit ×2 = $50, minus 20% of 100 = $20 loss ×2 = $40, net +$10. Clean, tempting, wrong — because "profit of his cost" means the base is cost, and cost isn't $100.
 Why it's a loss even though the rates (25 vs 20)  look  like a net gain:  the losing books had a  higher cost  ($125) than the winning books ($80). You're gaining 25% on a small base and losing 20% on a large base, so the dollar loss ($50) beats the dollar gain ($40). Percentages on different bases don't net out to their difference.

A bookseller sold 4 rare books for $100 each. He made a profit of 25%

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A bookseller sold 4 rare books for $100 each. He made a profit of 25%

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