A pen was sold at 10% loss. If the selling price was $6 more then the

Question

A pen was sold at 10% loss. If the selling price was $6 more then the seller could have made a profit of 5%. What was the purchase price of the pen?

(A) 45
(B) 40
(C) 30
(D) 25
(E) None of these.

chetan2u · Accepted Answer

Hi...

You can make the Q very simple if you realize that both loss% and profit % are on cost or purchase price ..
So an addition of $6 gets it from -10% to +5%, so a change of 15% in purchase price (P).
So 15%of P=6.......
P= 6*\frac{100}{15}=40

B

generis · Answer

Algebra 
Let purchase price (cost) = P

A pen sold at 10 percent loss means it was sold at 90 percent of P = .90P

If sold at 5 percent profit = 1.05P

It  was  sold at .90P
IF sold for $6 more: 90P + 6...
It would make a 5% profit: 1.05P

.90P + 6 = 1.05P
6 = .15P
P =  \frac{6}{.15}= 40

ANSWER B

Answer choices

Start with C) 30

At a 10 percent loss, it sold for: 
($30)(.9)= $27

IF sold at 5 percent profit: 
(1.05)($30) = $31.50

The difference between loss price and 5% profit price should be $6: 
$31.50 - 27 = $4.50

Too low. That means the base, 30, from which percentages are drawn, is too low (greater number yield greater difference between percentages).

But: $4.50 is 3/4 of $6.00. 
$30 is 3/4 of $40.

Try B) 40

Sold at 10 percent loss: 
(.90)($40) = $36

IF sold at 5 percent profit: 
(1.05)($40) = $42

($42 - $36) = $6 
That's the answer

ANSWER B

ScottTargetTestPrep · Answer

We can let r = revenue and c = cost. Since the pen was sold at a 10% loss:

r - c = -0.1c

r = 0.9c

Since if the selling price was $6 more then the seller could have made a profit of 5%:

r + 6 - c = 0.05c

r + 6 = 1.05c

Thus:

0.9c + 6 = 1.05c

6 = 0.15c

40 = c

Answer: B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A pen was sold at 10% loss. If the selling price was $6 more then the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A pen was sold at 10% loss. If the selling price was $6 more then the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards