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    Question

    Each of the questions given below has one question and two statements marked I and II. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer.

    The ratio of ages of A and B is 4:5 and that of B and C

    is 3:2. Find the age of B after 10 years. Statement I: Difference between the ages of C and A after 10 years and the difference between ages of A and B after 10 years is same. Statement II: Difference between ages of A and C is 4 years.
    A Only I and II Correct Answer Incorrect Answer
    B Only II Correct Answer Incorrect Answer
    C Only I Correct Answer Incorrect Answer
    D Either Statement I or II alone is sufficient. Correct Answer Incorrect Answer
    E Neither I nor II Correct Answer Incorrect Answer

    Solution

    ATQ,

    We are given: The ratio of ages of A and B 4:5. The ratio of ages of B and C is 3:2. We are tasked with finding B's age after 10 years. Let:

    A's age = 4x B's age = 5x, C's age = 10x/3.

    Statement I The difference between the ages of C and A after 10 years is the same as the difference between the ages of A and B after 10 years. This implies: (C+10)−(A+10)=(B+10)−(A+10). C−A=B−A. Substituting the values in terms of x:

    Solving for x determines A,B, and C's ages. Statement I is sufficient.

    The difference between C and A is 4 years: C − A = 4. Substituting values: Simplify:

    Solving for x determines A,B, and C's ages. Statement II is sufficient.

    Either Statement I or II alone is sufficient.

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