Solving Age-Related Word Problems: A Comprehensive Guide

Introduction

Age-related word problems often require careful attention to detail and the use of algebraic equations to find solutions. These types of problems can be found in various contexts, from academic examinations to standardized tests like the GMAT. In this article, we will explore a step-by-step approach to solving these problems, using examples and detailed explanations. By understanding the underlying principles, you can improve your problem-solving skills and ensure accurate results.

Example Problem and Solution

Problem Statement

Avanthi’s age is 1/6th of her father’s age. Her father’s age will be twice of Kapil’s age after 10 years. If Kapil’s eighth birthday was celebrated two years ago, what is Avanthi’s present age?

Step-by-Step Solution

Kapil's Current Age

1. Kapil's 8th birthday was celebrated 2 years ago, so Kapil is currently 10 years old.

Avanthi's Father's Age

2. Avanthi's father's age will be twice of Kapil's age after 10 years. Kapil's age after 10 years will be 20. Therefore, Avanthi's father's age will be 40.

Avanthi's Present Age

3. Avanthi's age is 1/6th of her father's age. Her father's age is 40. Therefore, Avanthi's age is 40 / 6 6.67 years.

Conclusion

So, Avanthi’s present age is 6.67 years.

Additional Examples and Problem-Solving Techniques

Example 1

Let the father’s age be x.
Ayisha’s age x/6
Shankar’s age is 82 10yrs
After 10 years:

x 10 2 * (10 10) x 10 40, hence x 30 years Ayisha’s present age is 30 / 6 5 years

Example 2

Let the present age of the father X years
Present age of the son Y years
10 years ago:

Age of the father X - 10 Age of the son Y - 10 ATQ (As the Question Tells): 7Y - 10 X - 10 7Y - 70 X - 10 X - 7Y -60 1 X^2 5Y^2 X^2 5Y^10 X - 5Y 8 2 Subtract equation 1 from 2: 2Y 68, hence Y 34 X - 5 * 34 8, hence X 170 - 8 162 Therefore, the father's current age is 170 - 6 164, and the son's current age is 162 / 4 40.25 years

Example 3

Let the present ages of Jaya be J, her mother's S, and Riya's R:

M - 2 4J or M 4J 2 M 2R 10 2R 20, hence R 12 - 2 10 So, M 2 * 10 20 42 years J M - 2 / 4 42 - 2 / 4 10.5 years

Jaya is presently 10.5 years old.

Example 4

Kamlesh's present age 58 13. After 6 years, his age will be 13 * 6 19. So, the father's age will be 38 years. Therefore, present age of the father is 38 - 6 32 years. So, Mahesh / Maheshwari's present age is 32 / 4 8 years.

Example 5

Let Ayisha's present age be X years
Ayisha's father's age 6X years
Shankar's age after 10 years 6X / 2 3X years
Shankar's present age 3X - 10 years
Shankar's eighth birthday was celebrated two years before hence Shankar's present age 8 - 2 10
3X - 10 10
3X 10 * 10
X 20 / 3 6.67

Ayisha's present age 6.67 years.

Example 6

Let Ayisha's age X
Father's age 6X
After 10 years, father's age 6X 10
Shankar's age (3X - 5) 10
Ayisha's age 5
Father's age 5 * 6 30

Example 7

Let Ayisha's present age is X, then father's present age is 6X
After 10 years, father's age is 6X 10
Shankar's age after 10 years is half of Ayisha's father's age, which is equal to (3X - 5), then current age of Shankar is 3X - 5
Shankar's age 2 years back is 8 years, then present age is 10 years
3X - 5 10
X 5

Ayisha's present age 5 years.