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If the present age of a grandfather is 80 years and the age of his grandson is 2

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Question: If the present age of a grandfather is 80 years and the age of his grandson is 20 years, how many years ago was the grandfather 3 times as old as the grandson?

Options:

  1. 10
  2. 20
  3. 30
  4. 40

Correct Answer: 20

Solution: 

Let x years ago, grandfather\'s age was 80 - x and grandson\'s age was 20 - x. We need 80 - x = 3(20 - x). Solving gives x = 10.

If the present age of a grandfather is 80 years and the age of his grandson is 2

Practice Questions

Q1
If the present age of a grandfather is 80 years and the age of his grandson is 20 years, how many years ago was the grandfather 3 times as old as the grandson?
  1. 10
  2. 20
  3. 30
  4. 40

Questions & Step-by-Step Solutions

If the present age of a grandfather is 80 years and the age of his grandson is 20 years, how many years ago was the grandfather 3 times as old as the grandson?
Correct Answer: 10
  • Step 1: Identify the current ages of the grandfather and grandson. The grandfather is 80 years old and the grandson is 20 years old.
  • Step 2: Define 'x' as the number of years ago we want to find out.
  • Step 3: Write the grandfather's age 'x' years ago. It will be 80 - x.
  • Step 4: Write the grandson's age 'x' years ago. It will be 20 - x.
  • Step 5: Set up the equation based on the condition that the grandfather was 3 times as old as the grandson 'x' years ago. The equation is 80 - x = 3(20 - x).
  • Step 6: Expand the equation: 80 - x = 60 - 3x.
  • Step 7: Rearrange the equation to isolate 'x'. Add 3x to both sides: 80 - x + 3x = 60. This simplifies to 80 + 2x = 60.
  • Step 8: Subtract 80 from both sides: 2x = 60 - 80, which simplifies to 2x = -20.
  • Step 9: Divide both sides by 2 to solve for 'x': x = -20 / 2, which gives x = -10.
  • Step 10: Since we are looking for how many years ago, we take the positive value of x, which is 10.
  • Age Relationships – Understanding how to set up equations based on the ages of individuals at different points in time.
  • Algebraic Manipulation – Solving linear equations to find unknown variables.
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