Multiple choice

The present age of a woman is six times that of her only daughter, Anu. Her husband’s present age is two years more than seven times Anu’s present age. The average present age of Anu, her parents and her only brother ( who is youngest of all the four members) is 15 years. By how many years is Anu elder to her brother?

  1. 1

  2. 2

  3. 3

  4. Cannot be dtermined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Anu's age be x. Mother = 6x, Father = 7x + 2. Let brother be B. Average = (x + 6x + 7x + 2 + B) / 4 = 15. 14x + B + 2 = 60 => 14x + B = 58. If x=4, B=2. If x=3, B=16 (impossible). Anu is 4, brother is 2. Difference is 2.

AI explanation

Let Anu's present age be A, her mother's age be 6A, and her father's age be 7A + 2. Since the average age of Anu, her parents, and her brother is 15, their total age is 60; letting the brother's age be B, we have A + 6A + 7A + 2 + B = 60. This simplifies to 14A + B = 58. For the ages to be realistic where the mother was at least as old as Anu when Anu was born, 6A must be greater than A, and trying integer values for A shows that A = 4 works, making the brother 2 years old. Therefore, Anu is 4 - 2 = 2 years elder to her brother. The result is 2.

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