Multiple choice

Passage

Directions : In this problem, a question is given followed by two statements numbered I and II. Read the statements and determine which of them is/are sufficient/necessary to answer the question. Choose the correct option accordingly. Mark your answer as (a) if the question can be answered by using statement I alone, but cannot be answered by using statement II alone (b) if the question can be answered by using statement II alone, but cannot be answered by using statement I alone (c) if both statements I and II together are necessary to answer the question (d) if the question can be answered by using either of the two statements alone (e) if both the statements together are not sufficient to answer the question

Find the present ages of A and B, if the present age of B is 20% of A. I. After 5 years, the respective ratio of ages of A and B will be 15 : 4. II. Five years ago, the respective ratio of ages of A and B was 25 : 3.

  1. (a)

  2. (b)

  3. (c)

  4. (d)

  5. (e)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let A = 5x and B = x. Statement I: (5x+5)/(x+5) = 15/4 leads to 20x + 20 = 15x + 75, so 5x = 55, x = 11. Statement II: (5x-5)/(x-5) = 25/3 leads to 15x - 15 = 25x - 125, so 10x = 110, x = 11. Both statements independently allow solving for the ages.

AI explanation

Let A and B be the present ages, and from the prompt we know B = 0.2A. Statement I gives (A + 5) divided by (B + 5) equals 15 divided by 4, and substituting B gives (A + 5) divided by (0.2A + 5) equals 15 divided by 4. Solving this equation yields A = 15 and B = 3. Statement II gives (A - 5) divided by (B - 5) equals 25 divided by 3, and substituting B gives (A - 5) divided by (0.2A - 5) equals 25 divided by 3, which also yields the same result. Since either statement alone perfectly solves the system, the question can be answered by using either of the two statements alone.

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