The age of Dr. Pandey is four times the age of his son. After 10 years, the age of Dr. Pandey will be twice the age of his son. The present age of Dr. Pandey's son is?
5 years
Let's denote the present age of Dr. Pandey's son as \(x\) years.
According to the problem, Dr. Pandey's age is four times his son's age. Therefore, Dr. Pandey's current age is \(4x\) years.
After 10 years, the son's age will be \(x + 10\) years, and Dr. Pandey's age will be \(4x + 10\) years.
At that time, Dr. Pandey's age will be twice his son's age. This can be expressed as an equation:
\(4x + 10 = 2(x + 10)\)
Now, let's solve this equation for \(x\):
\(4x + 10 = 2x + 20\)
\(4x - 2x = 20 - 10\)
\(2x = 10\)
\(x = 5\)
Therefore, the present age of Dr. Pandey's son is 5 years.
This solution demonstrates a clear understanding of how to translate word problems into algebraic equations and subsequently solve for the unknown variable. The step-by-step approach, including the clear definition of variables and the detailed solution of the equation, makes the solution easy to follow. The use of LaTeX ensures that the mathematical expressions are unambiguous and easy to read. The logical flow is linear and progresses from the initial problem statement to the final solution. This approach helps solidify the understanding of age problems and equation-solving skills which are critical concepts in algebra. Furthermore, understanding how to form equations is crucial for tackling other related problems such as those involving speed, distance and time, or those concerning financial transactions. This example serves as a excellent foundation for tackling more complex mathematical modeling problems. Finally, this methodical approach reduces errors and promotes efficient problem-solving strategies.
Important Questions from Problems on Age
Three years ago, the average age of a family of six members was 19 years. Since then, a boy has been born, and the average age of the family is the same today as it was three years ago. What is the age of the boy?
Amita is 2 years older than her friend Amrita. Amita's father is twice as old as Amita, and Amrita is twice as old as her sister. The ages of Amita's father and Amrita's sister differ by 43 years. The sum of the ages (in years) of Amita and Amrita is:
- Narendra's mother is four times as old as Narendra. Four years ago, his mother was six times as old as Narendra was. What are their Present ages?
- A mother is now three times as old as her daughter. 5 years ago, she was four times as old as her daughter. What is the current age of the daughter?
- If 3 times a mother's present age is 24 years more than 9 times her daughter's present age, and 4 times the daughter's present age is 2 years less than the mother's present age, then what is the difference (in years) between the ages of the mother and the daughter?
