Find the cost price of the article Statement I The article is marked up by T and it is sold at disco...........

Quantitative Aptitude (SBI-PO) Data Sufficiency

Direction: Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer.

Find the cost price of the article.

Statement I: The article is marked up by T% and it is sold at discount of 20%. The profit earned on selling the article is 44%.

Statement II: If shopkeeper offers a discount of 40% on marked price, then he earns the profit of Rs. 16

Statement III: If shopkeeper doesn't offer any discount on marked price, then the selling price will be Rs. 160 more than the cost price of the article.

Only the data given in statements I and II together is sufficient to answer the question.

Only the data given in statements I and III together is sufficient to answer the question.

The data given in any two statements together is sufficient to answer the question.

The data given in all three statements I, II and III together is sufficient to answer the question.

The data given in all three statements I, II and III together is not sufficient to answer the question.

छोटे Courses बड़े Results

Master Data Sufficiency

Prepare through Micro-courses

Try Now

Explanation:

Let the cost price of the article be Rs. 100x, then
From statement I:
Marked Price = Rs. (100 + T)x
Selling Price = Marked price × (1 – 20%)
144x = (100 + T)x × (1 – 20/100)
⇒ 144 = (100 + T) × 0.8
⇒ 180 = 100 + T
⇒ T = 80
So, marked price = Rs. (100 + T)x = Rs. 180x
From statement II:
New selling Price = Marked price × (1 – 40%)
(100x + 16) = Marked price × 0.6
From statement III:
When shopkeeper doesn't offer any discount on marked price, then he sells the article on marked price.
Marked price = Cost price + Rs. 160 = Rs. (100x + 160)
From statements I and II together:
100x + 16 = Marked price × 0.6
⇒ (100x + 16) = 180x × 0.6
⇒ 16 = 8x
⇒ x = 2
∴ Cost price of the article = 100x = Rs. 200
So, data given in statements I and II together is sufficient to answer the question.
From statements I and III together:
(100x + 16) = Marked price × 0.6
180x = Rs. (100x + 160)
⇒ 80x = 160
⇒ x = 2
∴ Cost price of the article = 100x = Rs. 200
So, data given in statements I and III together is sufficient to answer the question.
From statements II and III together:
(100x + 16) = (100x + 160) × 0.6
⇒ (100x + 16) = 60x + 96
⇒ 40x = 80
⇒ x = 2
∴ Cost price of the article = 100x = Rs. 200
So, data given in statements II and III together is sufficient to answer the question.
Hence, the data given in any two statements together is sufficient to answer the question.