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%.

Difficulty: Easy

Correct Answer: Either statement I alone or statement II alone is sufficient.

Explanation:


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.

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