Multiple choice

A seller makes a profit of 90 rupees after giving a discount of 20% on a cycle. What is the cost price of cycle? I. Marked price is 2 times of cost price. II. The profit would have been 20%, if a discount of 40% was given.

  1. The data in statement I alone is sufficient to answer the question, while data in statement II alone is not sufficient to answer the question.

  2. 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.

  3. The data in statement I alone or statement II alone is sufficient to answer the question.

  4. The data in both statements I and II is not sufficient to answer the question.

  5. The data in both statements I and II together is necessary to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: Let CP = x. Then MP = 2x. With 20% discount, SP = 0.8 × 2x = 1.6x. Profit = 1.6x - x = 0.6x = 90, so x = 150. Statement I alone is sufficient. Statement II: With 40% discount, SP = 0.6 × 2x = 1.2x. Profit% = (1.2x - x)/x × 100 = 20%. This matches the given 20% profit, so Statement II alone is also sufficient (just confirms the pricing structure, which yields the same CP of 150).

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