Data Sufficiency — Profit on a Watch What is the profit earned by selling each watch for ₹ 15,675? I. The total cost price of 5 such watches equals the selling price of 4 such watches (at ₹ 15,675 each). II. Each watch is sold at a profit of 25%.
Correct Answer: Either statement I alone or statement II alone is sufficient.
Introduction / Context:We must judge sufficiency to compute the profit per watch given a selling price (SP) of ₹ 15,675. Each statement independently might let us compute cost price (CP), then profit = SP - CP.
Given Data / Assumptions:
- SP per watch = ₹ 15,675.
- Statement I: 5 * CP = 4 * SP (with SP known).
- Statement II: Profit percentage = 25% (on CP or equivalently SP = 1.25 * CP).
Concept / Approach:If CP can be derived, profit = SP - CP is uniquely determined. We check each statement independently.
Step-by-Step Solution:
Using I alone: 5*CP = 4*SP ⇒ CP = (4/5)*SP = 0.8*15,675 = 12,540. Profit = 15,675 - 12,540 = 3,135.Using II alone: SP = 1.25*CP ⇒ CP = SP/1.25 = 15,675/1.25 = 12,540. Profit = 3,135 (same value).Verification / Alternative check:Both independent routes yield the same CP and profit. No extra information is required beyond either statement.
Why Other Options Are Wrong:
- I alone sufficient or II alone sufficient — each is true, but since both are independently sufficient, the best choice is “Either alone is sufficient”.
- Both together needed: Not required.
- Even both not sufficient: Incorrect; each alone suffices.
Common Pitfalls:Mixing up 25% of SP vs of CP (profit% is on CP). Also, forgetting that 5 CP = 4 SP refers to SP per watch already given.
Final Answer:Either statement I alone or statement II alone is sufficient.