Multiple choice

A grandfather is ten times older than his grand daughter. He is also $54$ years older than her. Find their present ages.

  1. The present age of granddaughter is $6$ years and that of grandfather is $60$ years.
  2. The present age of granddaughter is $8$ years and that of grandfather is $80$ years.
  3. The present age of granddaughter is $7$ years and that of grandfather is $70$ years.
  4. The present age of granddaughter is $9$ years and that of grandfather is $90$ years.
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A Correct answer
Explanation

Let the granddaughter's age be x. The grandfather's age is 10x. We are given 10x = x + 54, so 9x = 54, which means x = 6. The grandfather is 60.

AI explanation

Let the granddaughter's present age be x years, making the grandfather's age 10x years. Using the second condition, the grandfather is 54 years older, giving the equation 10x = x + 54. Solving this yields 9x = 54, so x = 6. The granddaughter is 6 years old and the grandfather is 60 years old.

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