What is the marked price of the shirt? I. A shopkeeper purchases 2 same shirts…
2025
What is the marked price of the shirt?
I. A shopkeeper purchases 2 same shirts for 2200 Rs. and earns 55 Rs. per shirt after giving 23% discount.
II. A shopkeeper marks the price 36% more than the cost price and earns 200 Rs. after giving some discount.
- A.
The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
- B.
The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
- C.
Both statements I and II together are needed to answer the question; neither statement I alone nor statement II alone is sufficient.
- D.
The data in both the statements I and II together are not sufficient to answer the question.
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept: A statement in a Data Sufficiency item is “sufficient” only if the facts given IN THAT STATEMENT ALONE let you compute one single, unique numerical answer to the question — not a plausible answer, a specific one with no unknowns left over. Check each statement alone first; only if NEITHER statement alone succeeds do you go on to check whether combining both together resolves it. If one statement is already sufficient by itself, the item is settled right there — there is nothing left to gain by also bringing in the other statement.
Applying this to statement I:
Two identical shirts cost 2200 Rs. together, so the cost price of one shirt = 2200 / 2 = 1100 Rs.
A profit of 55 Rs. per shirt means the selling price = 1100 + 55 = 1155 Rs.
The shirt was sold after a 23% discount on the marked price, so the selling price is 77% of the marked price: Marked Price × 77% = 1155, giving Marked Price = 1155 / 0.77 = 1500 Rs.
Every quantity needed — cost, profit, and discount rate — is given, and they combine to one unique marked price, so statement I alone is sufficient.
Applying this to statement II:
Let the cost price of the shirt = x Rs.
The price is marked 36% above cost, so Marked Price = 136% of x = 1.36x.
A profit of 200 Rs. is earned after some (unstated) discount, so Selling Price = x + 200.
This is only one relationship connecting x to the profit — the discount rate that connects 1.36x to (x + 200) is never given, so x cannot be solved for, and 1.36x therefore has no single numeric value.
Statement II alone is not sufficient.
Cross-check on statement I: with Marked Price = 1500 Rs. and a 23% discount, the discount amount = 1500 × 23% = 345 Rs., so Selling Price = 1500 − 345 = 1155 Rs., and profit = 1155 − 1100 = 55 Rs. — exactly the profit stated, confirming the value.
Result: statement I alone already fixes a unique marked price (1500 Rs.), so the item is settled at that first check — there is no need to invoke statement II or a combined reading at all. Statement II alone, meanwhile, does not fix any single value. The correct choice is the one stating that statement I alone is sufficient and statement II alone is not.