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    Question

    The current age of 'Aman' is 87.5% greater than 'Bittu's' age. The ratio of Aman's age 3 years hence from now to Bittu's age 6 years hence from now is 8:5. If Bittu's age 10 years hence from now will be (4x + 10) years, which of the following statements is/are true about 'x'?

    I. Multiplying 'x' with any odd natural number is a possibility.

    II. 30 ÷ 8 of x + 20% of 30% of 25 = 12.5% of 15

    A Only I Correct Answer Incorrect Answer
    B Only II Correct Answer Incorrect Answer
    C Neither I nor II Correct Answer Incorrect Answer
    D Both I and II Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Let the present age of 'Bittu' be '8a' years. Present age of 'Aman' = 1.875 X 8a = '15a' years ATQ, [(15a+3)/(8a+6)] = (8/5) Or, 5 × (15a + 3) = 8 × (8a + 6) Or, 75a + 15 = 64a + 48 Or, 75a - 64a = 48 - 15 Or, 11a = 33 So, a = 3 Present age of 'Bittu' = 8a = 8 X 3 = 24 years Age of 'Bittu', 10 years hence from now = 24 + 10 = 4x + 10 So, x = (24/4) = 6 For statement I: 'x' is an even number, so 'x' multiplied by any natural number will be even, which means the unit-digit of the resultant number will always be even. Therefore, statement-I is false. For statement II: 30 ÷ 8 of x + 20% of 30% of 25 = 12.5% of 15 LHS = 30 ÷ 8 of x + 20% of 30% of 25 = 30 ÷ 8 of 6 + 20% of 30% of 25 = 30 ÷ (8 × 6) + 0.2 × 0.3 × 25 = (30/48) + 1.5 = (5/8) + (3/2) = (17/8) RHS = 12.5% of 15 = 0.125 × 15 = (15/8) So, LHS ≠ RHS So, statement-II is false. Therefore, both statement-I and statement-II are false

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