The Cost Price of 20 Articles is The Same as The Selling Price of x Articles GMAT Problem Solving

Question: The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is

1. 15
2. 16
3. 18
4. 25
5. 27

“The cost price of 20 articles is the same as the selling price of x articles”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Prep Plus 2021”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

Given:

• The cost price of 20 articles is the same as the selling price of x articles.

Condition:

• The profit is 25%,

Find Out:

• The value of x

Let us consider the cost price as “c”
As per the given question, the cost price of 20 items is the same as selling price of x.
Hence, we can say that 20c=x(1.25c) - Since the profit is 25%
=>20c / 1.25c=x
=>16=x or we can say x=16

Correct Answer: B

Approach Solution 2:

Let us first assume the cost price of each article.
Next, we need to find the selling price of each article with 25% profit.
This would involve x and we can find x from that equation.
We will assume that the cost price of each article is 1 unit.
Thus the total cost price would be:
20×1=20
Now on each article there should be a profit of 25%.
We will calculate what the price of each article with 25% profit will be if all those x articles are sold at 20 units.
The reason being the cost price of 20 articles is the same as the selling price of x articles.
Therefore, the price of each article if x articles are sold for 20 units will be 20/x
Now the profit should be 25%.
So the cost of each article would be (1+25/100)*1
So equating these two we would get,
20/x = (1+25/100)*1
Taking LCM and solving we would get
20/x = (100+25/100)*1
20/x = 125/100
Cancelling the common factors, we will get
4/x=¼
Cross-multiplying we get,
x=16

Correct Answer: B

Approach Solution 3:

We will assume that the cost price of each article is 1 unit. Thus the total cost price would be 

20×1=2020×1=20

Now on each article there should be a profit of 25%. So we will calculate what the price of each article with 25% profit will be if all those x articles are sold at 20 units. This is because the cost price of 20 articles is the same as the selling price of x articles.
Therefore, the price of each article if x articles are sold for 20 units will be 20/x

Now the profit should be 25%. So the cost of each article would be 

(1+25/100) × 1

So equating these two we would get,

20/x = (1+25/100) × 1

Taking LCM and solving we would get,

20/x = (100+25/100)×1

20/x= (125/100)

Cancelling the common factors, we will get,

4/x = 1/4

Cross-multiplying we get,
x=16.

Correct Answer: B

Suggested GMAT Problem Solving Questions

• If x and y are positive integers and (1/7)^x * (1/8)^12 = (1/8)^1/18y, then what is the value of y-x? GMAT Problem Solving
• At Springfield High, three-fourths of the male students and half of the female students speak a foreign language GMAT Problem Solving
• What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 or by 35? GMAT Problem Solving
• If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving
• If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving
• A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving
• A conference room is equipped with a total of 45 metal or wooden chairs. GMAT Problem Solving 
• A welder received an order to make a 1 million litre cube-shaped tank. GMAT Problem Solving 
• After 6 games, Team B had an average of 61.5 points per game. GMAT Problem Solving 
• If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a three-percent vinegar solution, GMAT Problem Solving 
• A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. GMAT Problem Solving
• A circle is inscribed in a square with the diagonal of 4 centimeters. GMAT Problem Solving
• At a dog competition, a dog is awarded 10 points if it runs through 4 pipes, makes 10 jumps, and walks on 2 beams. GMAT Problem Solving 
• Two consultants, Mary and Jim, can type up a report in 12.5 hours and edit it in 7.5 hours. GMAT Problem Solving 
• Simplify:\frac{4.5-2*\frac{3}{6}+\frac{1}{4^2}}{0.75} GMAT Problem Solving 
• There are 6 points on xy-plane. GMAT Problem Solving 
• Mike, Tom, and Walt are working as sales agents for an insurance company. GMAT Problem Solving 
• A Commonwealth condominium complex has k apartments, n of which are rented at s dollars a month, GMAT Problem Solving 
• The Figure Below Shows a Square Inscribed in a Circle with the Radius of√6. What is the Area of the Shaded Region? GMAT Problem Solving 
• What is the value of k if the sum of consecutive odd integers from 1 to k equals 441? GMAT Problem Solving