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

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New post 15 Oct 2017, 21:52
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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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Oct 2017, 21:57, edited 1 time in total.
Renamed the topic.

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RockySinha wrote:
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.



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
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New post 16 Oct 2017, 04:51
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RockySinha wrote:
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.

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

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New post 17 Oct 2017, 11:42
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RockySinha wrote:
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.


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
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