Question

Directions: The following question is accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions.

A person marks the price of an article as Rs. y. What is the cost price of the article?

Statement I: The marked price of the article is 80% more than its cost price and the person sells it at 2x% discount. 

Statement II: The person gains 8% if he sells the article at x% discount and his profit is Rs. 5y.

Statement III: The person loses 12% on selling the article at a discount of Rs. 217..

1. The data in statement I and statement II are sufficient to answer the question, while the data in statement III alone is not sufficient to answer the question.
2. The data in statement II alone is sufficient to answer the question, while the data in statement I and III is not sufficient to answer the question.
3. The data in statements I alone or in statement II alone is sufficient to answer the question, while the data in statement III alone is not sufficient to answer the question.
4. The data in all the statements I, II and III is not sufficient to answer the question.
5. The data in statements I and statement III are sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

Answer 1

Correct Answer - Option 3 : The data in statements I alone or in statement II alone is sufficient to answer the question, while the data in statement III alone is not sufficient to answer the question.

Given:

Marked price of the article = Rs. y

Formula Used:

SP = CP ± Profit/Loss

SP = MRP × (1 - D%/100)

SP = CP × (1 ± (P%/L%)/100)

where, CP → Cost price, SP → Selling price, MRP → Marked price

Calculations:

Marked price of the article = Rs. y

Statement I:

MRP more than CP = 80%

Discount = 2x%

Now, MRP = (180/100) × CP

⇒ CP = Rs. y × (5/9) = Rs. 5y/9

So, Statement I is sufficient to answer the question.

Statement II:

Gain = 8%

Discount = 2x%

Profit = Rs. 5y

Now, Value of 8% = Rs. 5y

⇒ CP = 100% = Rs. 5y × (100/8)

⇒ CP = Rs. 125y/2

So, Statement II is sufficient to answer the question.

Statement III.

Loss = 12%

Discount = Rs. 217

No other information is given in the question

So, Statement III is not sufficient to answer the question.

∴ The data in statement I alone or in statement II alone is sufficient to answer the question, while the data in statement III alone is not sufficient to answer the question.