Find the difference between selling price of article Y and marked price of…
2022
Find the difference between selling price of article Y and marked price of article X. To find the difference which statement/s is/are required.
(A) Selling price of article X is Rs.140 more than that of article Y and article X is markup by Rs.264.
(B) Discount given on article Y is Rs. 56 more than the profit earned on article X.
(C) Selling price of article Y is Rs.224 more than the cost price of article Y. Discount given on article X is 30% and profit earned on article Y is 40%.
- A.
Only (A)
- B.
Both (A) & (C) together
- C.
Only (C)
- D.
Both (B) & (C) together
- E.
Both (A) & (B) together
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept
This is a data-sufficiency problem: the task is not to compute a number, but to decide the smallest set of given statements that pins down both quantities asked for. A target value is determinable only when every unknown feeding into it is fixed by the chosen statements. Here the target is the difference between the selling price of Y and the marked price of X, so we must be able to fix the selling price of Y (SPY) and the marked price of X (MPX).
Useful relations:
Profit% on cost: SP = CP × (1 + profit%).
Discount% on marked price: SP = MP × (1 − discount%).
Applying the statements
From statement C: It gives SPY − CPY = 224 and profit on Y is 40%, so SPY = 1.40 × CPY. Then 0.40 × CPY = 224, giving CPY = 560 and SPY = 784. Statement C also supplies the discount rate on X (30%). So C alone fixes SPY, but for X it gives only a rate and no absolute figure, so MPX stays open.
From statement A: SPX = SPY + 140, and X is marked up by Rs.264, i.e. MPX = CPX + 264. Alone, A only relates unknown prices and has no absolute value, so by itself it fixes nothing numerically.
Combining A with C: SPY = 784 (from C) gives SPX = 784 + 140 = 924 (from A). The 30% discount on X (from C) means SPX = 0.70 × MPX, so MPX = 924 ÷ 0.70 = 1320. Both required quantities are now fixed, and SPY − MPX = 784 − 1320 = −536 (a gap of 536). The markup-264 fact from A is consistent but not even needed once the discount rate fixes MPX, so A and C together are sufficient.
Why the other groupings fall short
C on its own: fixes SPY but leaves X with only a discount rate and no absolute price, so MPX cannot be found.
A on its own: only links the two selling prices and the markup to an unknown cost, with no absolute number anywhere, so nothing can be evaluated.
B with C: C does anchor Y to absolute values, but B compares the discount on Y with the profit on X and so introduces fresh unknowns (profit on X, discount on Y, and MP of Y) instead of tying X's marked price to a number; MPX is left free.
A with B: neither statement carries C's 224-figure or 40% profit, so Y is never anchored to absolute values; everything stays relative and no rupee value can be computed.
Result
Only the pairing that uses statement A together with statement C makes both SPY and MPX fully determinable, so that grouping is the required answer.