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Ram sells three articles A, B and C at profit of 10%, 20% and 30%, respectively. If the total profit he earns is 25% of the total cost, then how many of the following statements will necessarily hold true?
i. A was the least expensive article.
ii. B was the most expensive article.
iii. C was the most expensive article.
iv. B was the least expensive article.
  • a)
    0
  • b)
    1
  • c)
    2
  • d)
    4
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Ram sells three articles A, B and C at profit of 10%, 20% and 30%, res...
Let the cost prices of the three articles A, B and C are jc, y and z, respectively.
We have,

Simplifying, we get:
z = y + 3x
Therefore, C was the most expensive of the three articles.
Therefore, statement 3 is necessarily true.
Therefore, statement 2 is incorrect.
The other statements may or may not be true.
Hence, option 2.
This question is part of UPSC exam. View all CAT courses
Most Upvoted Answer
Ram sells three articles A, B and C at profit of 10%, 20% and 30%, res...
To solve this question, let's assume the cost price of articles A, B, and C as x, y, and z respectively.

Profit on article A = 10% of x = 0.1x
Profit on article B = 20% of y = 0.2y
Profit on article C = 30% of z = 0.3z

According to the given information, the total profit earned is 25% of the total cost. So, we can write the equation as:

0.1x + 0.2y + 0.3z = 0.25(x + y + z)

Simplifying this equation, we get:

0.1x + 0.2y + 0.3z = 0.25x + 0.25y + 0.25z

0.15x + 0.05y - 0.05z = 0

Now, let's analyze the statements one by one:

i. A was the least expensive article.
To analyze this statement, we need to compare the cost of article A with the costs of articles B and C. However, no information is given about their respective costs. Therefore, we cannot determine whether A is the least expensive article or not. This statement may or may not hold true.

ii. B was the most expensive article.
To analyze this statement, we need to compare the cost of article B with the costs of articles A and C. However, no information is given about their respective costs. Therefore, we cannot determine whether B is the most expensive article or not. This statement may or may not hold true.

iii. C was the most expensive article.
To analyze this statement, we need to compare the cost of article C with the costs of articles A and B. However, no information is given about their respective costs. Therefore, we cannot determine whether C is the most expensive article or not. This statement may or may not hold true.

iv. B was the least expensive article.
To analyze this statement, we need to compare the cost of article B with the costs of articles A and C. However, no information is given about their respective costs. Therefore, we cannot determine whether B is the least expensive article or not. This statement may or may not hold true.

Therefore, out of the given statements, none of them necessarily hold true. The correct answer is option (a) 0.
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Ram sells three articles A, B and C at profit of 10%, 20% and 30%, respectively. If the total profit he earns is 25% of the total cost, then how many of the following statements will necessarily hold true?i. A was the least expensive article.ii. B was the most expensive article.iii. C was the most expensive article.iv. B was the least expensive article.a)0b)1c)2d)4Correct answer is option 'B'. Can you explain this answer?
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