Multiple choice

Directions: The question below is followed by three statements (I), (II) and (III). You have to determine which statement(s) is/are sufficient/necessary to answer the question. What will be the sum of ages of A and B, if A is younger than B? Statements: I. 10 years ago, the age of B was twice the age A. II. 10 years from now, the ratio of the age of A to that of B will be 3 : 4. III. The ratio of the present age of B to that of A is 3 : 2.

  1. Any two of the statements

  2. II and III together

  3. I and III together

  4. I and II together

  5. None of the given statement
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A Correct answer
Explanation

Let A and B be the present ages. Statement I gives (B-10) = 2(A-10) -> B = 2A - 10. Statement II gives (A+10)/(B+10) = 3/4 -> 4A + 40 = 3B + 30. Statement III gives B/A = 3/2 -> B = 1.5A. Any two statements provide a system of two linear equations with two variables, which is sufficient to solve for A and B.

AI explanation

Let the present ages of A and B be a and b. Statement I provides the equation b - 10 = 2(a - 10), which simplifies to b = 2a - 10. Statement II provides the proportional equation (a + 10) / (b + 10) = 3 / 4, which can be solved alongside equation I to find their exact ages. Statement III provides the equation b / a = 3 / 2, which forms a solvable linear system when paired with either statement I or statement II. Because any pair of statements uniquely determines the values of a and b, any two statements are sufficient to find the required sum.

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