Multiple choice

Directions: The question given below is followed by two statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Three friends X, Y and Z invested Rs. 52,000 in a fund in the ratio 2 : 1 : 3. What is the profit earned by each of them? I. Z got Rs. 2000 in profit more than X. II. Z got Rs. 6000 as his share in profit.

  1. The question can be answered by using statement I alone but cannot be answered by using statement II alone.

  2. The question can be answered by using statement II alone but cannot be answered by using statement I alone.

  3. Both statements I and II together are required to answer the question.

  4. The answer can be found by using any of the two statements alone.

  5. Both the statements together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Ratio 2:1:3 means total parts = 6. Total profit = 52000. Each share: X=17333.33, Y=8666.67, Z=26000. Statement I: Z-X = 2000. Ratio 3x-2x = x = 2000. Total = 6*2000 = 12000. Statement II: Z = 6000. Ratio 3x = 6000, x = 2000. Both are sufficient individually.

AI explanation

The total investment ratio of 2:1:3 means the profit will be distributed in the exact same proportion. Statement II directly provides Z's share as Rs. 6000, so since 3 parts equal 6000, we can calculate that 1 part is 2000 and 2 parts is 4000 to find everyone's share. Statement I states Z got Rs. 2000 more than X, which perfectly aligns with the ratio difference of 1 part (3 - 2), meaning 1 part equals 2000, allowing us to calculate all individual shares; therefore, either statement alone is sufficient.

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