Multiple choice

The age of the father of two children is twice that of the elder one added to four times that of the younger one. If the geometric mean of the ages of the children is $4\sqrt 3 $ and their harmonic mean is 6, then father's age is

  1. 36

  2. 40

  3. 50

  4. 56
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let ages be x and y. Geometric mean sqrt(xy) = 4*sqrt(3) => xy = 48. Harmonic mean 2xy/(x+y) = 6 => 2(48)/(x+y) = 6 => x+y = 16. Solving x+y=16 and xy=48 gives x=12, y=4. Father's age = 2(12) + 4(4) = 24 + 16 = 40.

AI explanation

Let the children's ages be x and y. Their geometric mean is the square root of their product, so xy = (4 times square root of 3) squared = 48. The harmonic mean formula gives 2xy divided by (x plus y) = 6, which simplifies to 96 = 6x plus 6y, so x plus y = 16. Solving the equations x plus y = 16 and xy = 48 gives the ages as 12 and 4. The father's age is 2(12) + 4(4) = 40.

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