# Ages

**Ages**

In quantitative ability, questions related to ages often involve finding the current age of a person, determining the age of someone in the past or future, or solving problems involving the age of multiple individuals. These questions can be tricky, but with the right approach, they can be easily solved.

Let's go through some common types of age-related questions along with their solutions:

**Present Age Problems:**

These questions involve finding the current age of an individual given some information. Typically, you'll be provided with the age of a person at a certain time and some additional details. You need to use this information to calculate the person's current age.

Example 1:

Five years ago, Alice was three times as old as Bob. If Alice is 30 years old now, find Bob's current age.

Solution 1:

Let's assume Bob's current age is x years.

Five years ago, Bob's age was (x - 5) years.

According to the given information, Alice was three times as old as Bob five years ago, so Alice's age five years ago was 3(x - 5) years.

Since Alice is currently 30 years old, her age five years ago was 30 - 5 = 25 years.

Now, set up an equation:

3(x - 5) = 25

3x - 15 = 25

3x = 25 + 15

3x = 40

x = 40 / 3

x = 13.33 (approximately)

So, Bob's current age is approximately 13 years.

**Age Difference Problems:**

These questions involve finding the age difference between two individuals at a specific time.

Example 2:

Five years ago, the age of John was twice the age of Mary. If the difference in their ages remains the same, what is the current age difference between John and Mary?

Solution 2:

Let's assume John's current age is J years, and Mary's current age is M years.

Five years ago, John's age was (J - 5) years, and Mary's age was (M - 5) years.

According to the given information, the age difference between John and Mary five years ago was J - 5 - (M - 5) = J - M.

Since the age difference remains the same, the current age difference between John and Mary will also be J - M.

**Age Ratio Problems:**

These questions involve finding the ratio of ages between individuals at a certain time.

Example 3:

The ratio of the ages of Sarah and Tom is 3:5. Five years ago, the ratio of their ages was 5:9. Find their current ages.

Solution 3:

Let's assume Sarah's current age is 3x years and Tom's current age is 5x years.

Five years ago, Sarah's age was 3x - 5 years, and Tom's age was 5x - 5 years.

According to the given information, the ratio of their ages five years ago was 5x - 5 : 9.

So, we have the equation:

(3x - 5) / (5x - 5) = 5 / 9

Solving the equation, you can find the value of x and then calculate Sarah and Tom's current ages.

Example 4 :

Five years ago, the age of a family of four members in terms of the eldest, second eldest, third eldest, and youngest were in the ratio 5:4:3:2. If the youngest is 8 years old now, find the current age of the eldest.

Solution 4 :

Let the youngest's age be x years.

Five years ago, the ages of the family members were:

Eldest = 5x

Second eldest = 4x

Third eldest = 3x

Youngest = x

According to the given information, the ratio of their ages five years ago was 5:4:3:2. So, we have the equation:

(5x - 5) / (4x - 5) = (4x - 5) / (3x - 5) = (3x - 5) / (x - 5) = 5 / 4

Solving the equation:

(5x - 5) * (3x - 5) = (4x - 5) * (4x - 5)

15x^2 - 40x + 25 = 16x^2 - 40x + 25

15x^2 - 16x^2 = 0

x^2 = 0

x = 0 (Ignoring the solution x = 0 since age cannot be zero)

Now, we have the youngest's age (x) as 8 years.

Eldest's current age = 5x = 5 * 8 = 40 years

These are some common types of age-related problems you may encounter in quantitative ability tests. To solve such problems effectively, carefully read the questions, set up the necessary equations, and solve step by step to find the correct answers. Practice will help you improve your problem-solving skills and accuracy in age-related quantitative ability questions.