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A mother is 4 times as old as her daughter. After 8 years, the mother will be tw

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Question: A mother is 4 times as old as her daughter. After 8 years, the mother will be twice as old as her daughter. What is the present age of the daughter?

Options:

  1. 4
  2. 8
  3. 12
  4. 16

Correct Answer: 8

Solution: 

Let the daughter\'s age be x. Then the mother\'s age is 4x. In 8 years, 4x + 8 = 2(x + 8). Solving gives x = 8.

A mother is 4 times as old as her daughter. After 8 years, the mother will be tw

Practice Questions

Q1
A mother is 4 times as old as her daughter. After 8 years, the mother will be twice as old as her daughter. What is the present age of the daughter?
  1. 4
  2. 8
  3. 12
  4. 16

Questions & Step-by-Step Solutions

A mother is 4 times as old as her daughter. After 8 years, the mother will be twice as old as her daughter. What is the present age of the daughter?
Correct Answer: 8
  • Step 1: Let the daughter's current age be represented by 'x'.
  • Step 2: Since the mother is 4 times as old as her daughter, we can express the mother's age as '4x'.
  • Step 3: In 8 years, the daughter's age will be 'x + 8'.
  • Step 4: In 8 years, the mother's age will be '4x + 8'.
  • Step 5: According to the problem, in 8 years, the mother will be twice as old as the daughter. We can write this as the equation: '4x + 8 = 2(x + 8)'.
  • Step 6: Now, simplify the equation: '4x + 8 = 2x + 16'.
  • Step 7: Subtract '2x' from both sides to get: '2x + 8 = 16'.
  • Step 8: Next, subtract '8' from both sides: '2x = 8'.
  • Step 9: Finally, divide both sides by '2' to find 'x': 'x = 4'.
  • Step 10: Therefore, the present age of the daughter is 4 years.
  • Algebraic Equations – The problem involves setting up and solving linear equations based on relationships between ages.
  • Age Problems – This is a classic age problem where the relationship between the ages of two individuals is analyzed over time.
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