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Bunuel
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An article is sold at 20% profit. If its cost price is increased by $5 25 Jun 2019, 02:19
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B
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95% (hard)

Question Stats:

49% (02:57) correct 51% (03:25) wrong based on 150 sessions

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An article is sold at 20% profit. If its cost price is increased by $50 and at the same time, if its selling price is also increased by $30, the percentage of profit decreases by \(\frac{10}{3}\)%. Find the cost price.

(A) 650
(B) 850
(C) 1000
(D) 3000
(E) 4500
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B
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PKN
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An article is sold at 20% profit. If its cost price is increased by $5 25 Jun 2019, 12:45
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Bunuel
An article is sold at 20% profit. If its cost price is increased by $50 and at the same time, if its selling price is also increased by $30, the percentage of profit decreases by \(\frac{10}{3}\)%. Find the cost price.

(A) 650
(B) 850
(C) 1000
(D) 3000
(E) 4500
Show more

Initial scenario:-
Let the CP be 'x'.
SP=1.2x

Amended scenario:-
CP=x+50
SP=1.2x+30

%Profit=\(20-\frac{10}{3}=\frac{50}{3}%\)
Or, \(\frac{1.2x+30-x-50}{x+50}*100=\frac{50}{3}\)
Or, 6(0.2x-20)=x+50
Or, 1.2x-120=x+50
Or, 0.2x=170
\(x=\frac{1700}{2}=850\)

Ans. (B)
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An article is sold at 20% profit. If its cost price is increased by $5 10 Dec 2020, 15:37
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Why are we dividing by the cost price? Isn't profit equal to (Selling Price - Cost Price)/(Selling Price)?
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An article is sold at 20% profit. If its cost price is increased by $5 16 Dec 2020, 12:10
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Bunuel
An article is sold at 20% profit. If its cost price is increased by $50 and at the same time, if its selling price is also increased by $30, the percentage of profit decreases by \(\frac{10}{3}\)%. Find the cost price.

(A) 650
(B) 850
(C) 1000
(D) 3000
(E) 4500
Show more
Solution:

Let the original cost of the article be c. Since the article is sold at a 20% profit, the profit is 0.2c, and the sale price is 1.2c.

If the cost is increased by $50 and the selling price is increased by $30, then the new profit is (1.2c + 30) - (c + 50) = 0.2c - 20.

We are also told that the profit decreases by 10/3 %; thus, the new profit is 20 - 10/3 = 50/3 %.

Recall that the new cost is c + 50 and the new profit is 0.2c - 20; thus, in terms of c, the percentage of profit is [(0.2c - 20) / (c + 50)] * 100. Let’s set this expression equal to 50/3:

[(0.2c - 20)/(c + 50)] * 100 = 50/3

(0.2c - 20)/(c + 50) = 50/300 = 1/6

1.2c - 120 = c + 50

0.2c = 170

c = 170/0.2 = $850

Answer: B
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An article is sold at 20% profit. If its cost price is increased by $5 16 Dec 2020, 12:38
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enochan319
Why are we dividing by the cost price? Isn't profit equal to (Selling Price - Cost Price)/(Selling Price)?
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Profit = SP - CP

or

Profit % = (SP-CP)/CP * 100

Hope it helps!
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An article is sold at 20% profit. If its cost price is increased by $5 01 Oct 2024, 12:26
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ScottTargetTestPrep
Bunuel
An article is sold at 20% profit. If its cost price is increased by $50 and at the same time, if its selling price is also increased by $30, the percentage of profit decreases by \(\frac{10}{3}\)%. Find the cost price.

(A) 650
(B) 850
(C) 1000
(D) 3000
(E) 4500
Solution:

Let the original cost of the article be c. Since the article is sold at a 20% profit, the profit is 0.2c, and the sale price is 1.2c.

If the cost is increased by $50 and the selling price is increased by $30, then the new profit is (1.2c + 30) - (c + 50) = 0.2c - 20.

We are also told that the profit decreases by 10/3 %; thus, the new profit is 20 - 10/3 = 50/3 %.

Recall that the new cost is c + 50 and the new profit is 0.2c - 20; thus, in terms of c, the percentage of profit is [(0.2c - 20) / (c + 50)] * 100. Let’s set this expression equal to 50/3:

[(0.2c - 20)/(c + 50)] * 100 = 50/3

(0.2c - 20)/(c + 50) = 50/300 = 1/6

1.2c - 120 = c + 50

0.2c = 170

c = 170/0.2 = $850

Answer: B
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ScottTargetTestPrep Bunuel
Can you please explain how to figure % profit decrease by 10/3% as (20-10/3)% and not (20 - (10/3% of 20))?
Thank you!
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An article is sold at 20% profit. If its cost price is increased by $5 02 Oct 2024, 00:20
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Bunuel
An article is sold at 20% profit. If its cost price is increased by $50 and at the same time, if its selling price is also increased by $30, the percentage of profit decreases by \(\frac{10}{3}\)%. Find the cost price.

(A) 650
(B) 850
(C) 1000
(D) 3000
(E) 4500
Solution:

Let the original cost of the article be c. Since the article is sold at a 20% profit, the profit is 0.2c, and the sale price is 1.2c.

If the cost is increased by $50 and the selling price is increased by $30, then the new profit is (1.2c + 30) - (c + 50) = 0.2c - 20.

We are also told that the profit decreases by 10/3 %; thus, the new profit is 20 - 10/3 = 50/3 %.

Recall that the new cost is c + 50 and the new profit is 0.2c - 20; thus, in terms of c, the percentage of profit is [(0.2c - 20) / (c + 50)] * 100. Let’s set this expression equal to 50/3:

[(0.2c - 20)/(c + 50)] * 100 = 50/3

(0.2c - 20)/(c + 50) = 50/300 = 1/6

1.2c - 120 = c + 50

0.2c = 170

c = 170/0.2 = $850

Answer: B
ScottTargetTestPrep Bunuel
Can you please explain how to figure % profit decrease by 10/3% as (20-10/3)% and not (20 - (10/3% of 20))?
Thank you!
Show more

I agree, the phrasing is confusing, and the question could have been framed more clearly to avoid ambiguity.
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