SSC CGL Maths Arithmetic Ages-Based Questions with Solutions

SSC CGL Maths Questions often confuse students because they require tracking past, present, and future ages using ratios and simple algebra. Many learners struggle to form equations correctly or decide which method to apply in different scenarios. 

Understanding the core concepts and solving techniques through step-by-step examples helps identify common patterns, improve accuracy, and increase speed in solving SSC CGL Maths arithmetic ages questions for competitive exams.

SSC CGL Maths Arithmetic - Concept of  Age 

Age-based questions are a common part of the SSC CGL Quantitative Aptitude section. These questions test your ability to relate a person's age across different time periods using ratios, simple algebra, and logical reasoning. Most problems involve comparing Past, Present, and Future ages and converting the given information into mathematical equations.

Understanding how age changes with time is the first step toward solving these questions accurately. If a person's present age is represented by x, their age increases or decreases by the same number of years as time moves forward or backward. This basic concept forms the foundation for solving both simple and complex SSC CGL Maths Arithmetic Ages Questions.

If a person's Present Age is x, then:

• Age n years ago (Past) = x - n

• Age n years later (Future) = x + n

SSC CGL Maths Age Ratio Problems With Solutions

Age problems frequently appear in both Maths and Reasoning sections of competitive exams.

Below are some important age ratio questions with step-by-step solutions for better understanding:

Question 1: The ratio of the ages of father and son at present is 6: 1. After 5 years, the ratio will become 7 : 2. The present age of the son is:

(a) 10 years
(b) 9 years
(c) 6 years
(d) 5 years

Solution:

Present Ratio (Father : Son) = 6 : 1
Ratio after 5 years (Father : Son) = 7 : 2

Notice the change in the ratio parts from the present to 5 years later:

Father's change: 6 → 7 (+1 unit)
Son's change: 1 → 2 (+1 unit)

Since both father and son age at the same rate, an increase of 1 unit corresponds to 5 years:

1 unit = 5 years

The son's present age is represented by 1 unit in the present ratio:

Son's present age = 1 unit = 5 years

Correct Answer:
(d) 5 years

Question 2: The ratio of the ages of A and B at present is 4 : 3. Ten years earlier, the ratio was 3: 2. Find the present ages of A and B (in years).

(a) 40, 30
(b) 48, 36
(c) 64, 48
(d) 20, 15

Solution

Ratio 10 years ago (A : B) = 3 : 2
Present Ratio (A : B) = 4 : 3

Now observe the change in ratio units from 10 years ago to the present:

A's change: 3 → 4 (+1 unit)
B's change: 2 → 3 (+1 unit)

Since both A and B age equally over time, an increase of 1 unit corresponds to 10 years:

1 unit = 10 years

Now calculate present ages using the present ratio:

Present age of A = 4 units = 4 × 10 = 40 years
Present age of B = 3 units = 3 × 10 = 30 years

Correct Answer:
(a) 40, 30

Question 3: The ratio of the ages of A and B at present is 5 : 3. After 7 years, the ratio will become 3 : 2. What is the sum of the present ages of A and B?

(a) 46 years
(b) 48 years
(c) 56 years
(d) 58 years

Solution

Step 1: Equalize the ratio differences

Present Ratio (A : B) = 5 : 3
Difference between the ratio parts = 5 − 3 = 2 units

Ratio after 7 years (A : B) = 3 : 2
Difference between the ratio parts = 3 − 2 = 1 unit

Since the age difference between two people always remains constant, equalize the differences by multiplying the future ratio by 2:

New Future Ratio = (3 × 2) : (2 × 2) = 6 : 4

Step 2: Find the value of 1 unit

Now compare the present ratio with the updated future ratio:

Present Ratio = 5 : 3
Future Ratio = 6 : 4

Both A and B increase by 1 unit (5 → 6 and 3 → 4). Therefore:

1 unit = 7 years

Step 3: Calculate the sum of their present ages

Sum of the present ratio parts = 5 + 3 = 8 units

Therefore:

Sum of present ages = 8 × 7 = 56 years

Correct Answer:
(c) 56 years

Question 4: If the ratio of the ages of A and B at present is 2 : 1, and 6 years earlier the ratio was 3 : 1, what is the sum of the present ages of A and B?

(a) 24 years
(b) 26 years
(c) 34 years
(d) 36 years

Solution

Step 1: Equalize the ratio differences

Present Ratio (A : B) = 2 : 1
Difference between the ratio parts = 2 − 1 = 1 unit

Ratio 6 years ago (A : B) = 3 : 1
Difference between the ratio parts = 3 − 1 = 2 units

Since the age difference between two people always remains constant, equalize the differences by multiplying the present ratio by 2:

New Present Ratio = (2 × 2) : (1 × 2) = 4 : 2

Step 2: Find the value of 1 unit

Now compare the balanced present ratio with the past ratio:

Past Ratio (6 years ago) = 3 : 1
Present Ratio = 4 : 2

Both A and B increase by 1 unit (3 → 4 and 1 → 2). Therefore:

1 unit = 6 years

Step 3: Calculate the sum of their present ages

Using the balanced present ratio (4 : 2):

Sum of the ratio parts = 4 + 2 = 6 units

Therefore:

Sum of present ages = 6 × 6 = 36 years

Correct Answer:
(d) 36 years

Question 5: The ratio of the current ages of A and B is 7 : 8. After 6 years, the ratio of their ages will become 8 : 9. What is the present age of A?

(a) 56 years
(b) 52 years
(c) 42 years
(d) 40 years

Solution

Present Ratio (A : B) = 7 : 8
Ratio after 6 years (A : B) = 8 : 9

Now observe the change in the ratio units from the present to 6 years later:

A's change: 7 → 8 (+1 unit)
B's change: 8 → 9 (+1 unit)

Since both A and B age equally over time, an increase of 1 unit corresponds to 6 years:

1 unit = 6 years

The present age of A is represented by 7 units in the present ratio.

Present age of A = 7 × 6 = 42 years

Correct Answer:
(c) 42 years

Tips to Solve Arithmetic Ages Questions Faster

Solving age problems becomes easier when you follow a systematic approach. The tips below can help you avoid common mistakes and improve your speed and accuracy in the SSC CGL exam.

• Identify whether the question is based on past, present, or future age.

• Represent unknown ages using variables or ratio units.

• Keep the age difference constant, as it never changes over time.

• Form equations carefully before solving.

• Verify the final answer by substituting it back into the given conditions.