SSC CGL 2027 Average Questions Using the Replacement Method

Average is an important topic in Quantitative Aptitude for SSC CGL preparation. Questions may involve the average age of a group, marks scored by students, replacement of a person, changes in group size, and the effect of adding or removing values. The replacement method helps candidates solve many of these questions without calculating the entire total again.

In this guide, you will learn the average formula, the replacement shortcut, solved examples, common mistakes, and practice questions with answers for SSC CGL 2027 preparation.

1. What Is an Average?

The average represents the total of all values divided by the number of values. It gives a single value that describes the central level of a group.

Example: Find the average of 10, 20, 30, 40 and 50.

Sum = 10 + 20 + 30 + 40 + 50 = 150.

Number of values = 5.

Average = 150 ÷ 5 = 30.

Answer: 30.

2. What Is the Replacement Method?

The replacement method is used when one value in a group is replaced by another value. Instead of calculating the new total from the beginning, calculate the difference between the incoming and outgoing values.

Important: This shortcut applies when one value is replaced and the total number of values remains unchanged.

3. Solved Example: Replacing a Number

Question: The average of 8 numbers is 25. If the number 18 is replaced by 34, find the new average.

Solution:

Old average = 25.

Old number = 18.

New number = 34.

Change in value = 34 − 18 = 16.

Change in average = 16 ÷ 8 = 2.

New average = 25 + 2 = 27.

Answer: 27.

4. Solved Example: Replacement of a Person

Question: The average age of 10 people is 24 years. One person aged 30 years leaves the group and is replaced by a person aged 40 years. Find the new average age.

Solution:

Old average = 24 years.

Incoming age − Outgoing age = 40 − 30 = 10 years.

Change in average = 10 ÷ 10 = 1 year.

New average = 24 + 1 = 25 years.

Answer: 25 years.

Shortcut: Since the new person is 10 years older than the person leaving, the group's average age increases by 10 ÷ 10 = 1 year.

5. Solved Example: Replacement of a Student

Question: The average marks of 20 students increase by 2 when one student's marks are corrected. If the original marks were 45, find the corrected marks.

Solution:

Number of students = 20.

Increase in average = 2.

Increase in total marks = 20 × 2 = 40.

Corrected marks = 45 + 40 = 85.

Answer: 85 marks.

6. Solved Example: Finding the Number Replaced

Question: The average of 12 numbers is 35. One number is replaced by 59, and the new average becomes 38. Find the original number.

Solution:

Increase in average = 38 − 35 = 3.

Increase in total = 12 × 3 = 36.

The new number is 36 greater than the original number.

Original number = 59 − 36 = 23.

Answer: 23.

7. Average When a Value Is Added or Removed

When a value is added to or removed from a group, the number of values changes. In such questions, calculate the old total first and then apply the change.

Example 1: Adding a New Value

Question: The average of 5 numbers is 18. A sixth number, 30, is added. Find the new average.

Solution:

Old total = 5 × 18 = 90.

New total = 90 + 30 = 120.

New average = 120 ÷ 6 = 20.

Answer: 20.

Example 2: Removing a Value

Question: The average of 6 numbers is 22. If the number 32 is removed, find the average of the remaining numbers.

Solution:

Old total = 6 × 22 = 132.

Remaining total = 132 − 32 = 100.

Remaining numbers = 5.

New average = 100 ÷ 5 = 20.

Answer: 20.

8. Important Shortcuts for Average Questions

• Replacement shortcut: Divide the difference between the incoming and outgoing values by the group size.
• Find the total: Multiply the average by the number of values.
• Find a missing value: Calculate the required total and subtract the known values.
• Check the direction: Replacing a value with a larger value increases the average; replacing it with a smaller value decreases the average.
• Watch the group size: The replacement shortcut assumes the number of values stays constant.
• Use estimation: Estimate the expected average to catch calculation errors quickly.

9. Common Mistakes to Avoid

1. Dividing the difference by the wrong number of values.
2. Adding the difference to the average without dividing it by the group size.
3. Using the replacement shortcut when a value is simply added or removed.
4. Subtracting in the wrong order when finding the original value.
5. Forgetting that a lower incoming value decreases the average.

10. Practice Questions for SSC CGL 2027

Attempt these questions before checking the answer key.

Answer Key with Explanations

1. B) 26: Change = 35 − 15 = 20. Increase in average = 20 ÷ 10 = 2. New average = 24 + 2 = 26.

2. B) 33 years: Change = 35 − 20 = 15. Increase in average = 15 ÷ 15 = 1. New average = 32 + 1 = 33 years.

3. B) 44: Increase in average = 1. Increase in total = 8 × 1 = 8. Original number = 52 − 8 = 44. Therefore, the correct option is C) 44.

4. B) 17: Old total = 6 × 15 = 90. New total = 90 + 29 = 119. New average = 119 ÷ 7 = 17.

5. B) 22: Increase in average = 30 − 28 = 2. Increase in total = 12 × 2 = 24. Original number = 46 − 24 = 22.

11. How to Prepare Average Questions for SSC CGL

Start with the basic average formula and practise finding totals, missing values and group averages. Once you understand these concepts, move on to replacement problems involving ages, marks and numerical values.

Practise a small set of questions daily and record the errors you make. Focus on identifying whether the group size changes, whether a value is replaced, and whether the average should increase or decrease.

Check the official SSC CGL notification and syllabus when released for the applicable 2027 examination details. This article is a preparation resource and does not guarantee that a particular question will appear in the examination.

Frequently Asked Questions

1. What is the formula for average?

Average equals the sum of all values divided by the number of values.

2. What is the replacement method in average questions?

It calculates the change in average by dividing the difference between the incoming and outgoing values by the number of values.

3. When can the replacement shortcut be used?

Use it when one value is replaced by another and the total number of values remains unchanged.

4. How do you find a missing value using averages?

Multiply the average by the number of values to find the total, then subtract the known values from that total.

5. How can I solve average questions faster?

Learn the total-from-average formula, practise the replacement shortcut and check whether the group size changes.