Average
SSC-CGL Exams
1. Introduction
Average means equal distribution of total quantity among all items. It's one of the easiest yet high-scoring topics in SSC CGL — often mixed with weight, age, replacement, and data-based problems.
2. Basic Formula
Average = Sum of all items / Number of items
Example 1
Find the average of 10, 20, 30, 40, and 50.
Average = (10+20+30+40+50)/5 = 150/5 = 30
Average = 30
Example 2
If the average of 5 numbers is 40, find their total sum.
Sum = 40 × 5 = 200
Sum = 200
3. Effect of New/Removed Item
When an item is added or removed, use difference logic instead of re-calculating everything.
New average increases
Added number > old average
New average decreases
Added number < old average
Shortcut Formula (for removal or addition)
(New Average - Old Average) × Total number = Difference between number added/removed and old average
Example 3
Average of 10 students is 60. One score of 80 replaces a score of 40. Find the new average.
Change in average = (80 - 40)/10 = 4
New Average = 60 + 4 = 64
Example 4
Average of 8 numbers is 50. If one new number is added and new average becomes 52, find the number added.
(52 - 50) × 9 = 2 × 9 = 18
Added number = 18 + 50 = 68
Number added = 68
4. Weighted Average
Used when quantities are not equal (e.g., average marks of different subjects with different weights).
Weighted Average = (w₁x₁ + w₂x₂ + w₃x₃ + ...) / (w₁ + w₂ + w₃ + ...)
Example 5
A student scored 80, 70, and 90 in three subjects with weightages 2, 3, and 5 respectively. Find weighted average:
= (80×2 + 70×3 + 90×5) / (2+3+5) = (160 + 210 + 450)/10 = 820/10 = 82
Weighted Average = 82
5. Replacement Questions
These are very common in SSC exams — especially with milk–water or mixture-type questions.
Example 6
A vessel contains 40 L of pure milk. 8 L milk is replaced with water. Again 8 L mixture is removed and replaced with water. Find the final quantity of milk.
Formula: Remaining milk = V (1 - x/V)^n
V = 40, x = 8, n = 2
= 40(1 - 8/40)^2 = 40(0.8)^2 = 40×0.64 = 25.6
Milk left = 25.6 L
6. Short Tricks for SSC
| Case | Shortcut | Example |
|---|---|---|
| Average from total | Sum ÷ Count | 200 ÷ 5 = 40 |
| New item added | (Change in Avg × Total + Old Avg) | - |
| Weighted Avg (mixing) | (x₁n₁ + x₂n₂)/(n₁ + n₂) | - |
| Replacement (mixture) | Final = V(1 - x/V)^n | - |
| Average of consecutive numbers | (First + Last)/2 | - |
Example 7 (Shortcut Average of Consecutive Numbers)
Find the average of first 25 even numbers.
First = 2, Last = 50
Average = (2+50)/2 = 26
Average = 26
7. Practice Section
Q1. Find the average of 12, 18, 24, and 36.
View Answer
(12+18+24+36)/4 = 90/4 = 22.5
22.5
Q2. The average of 8 numbers is 45. If one number (60) is added, what is the new average?
View Answer
(60 - 45)/9 = +15/9 = +1.67 ⇒ New Avg = 46.67
46.67
Q3. The average weight of 10 men is 70 kg. If one man leaves and a new man joins, average becomes 71 kg. If the man who left weighed 65 kg, find the new man's weight.
View Answer
70×10 = 700; 71×10 = 710; 710 - (700 - 65) = 75
New man = 75 kg
Q4. Find weighted average of 10 and 30 with weights 2 and 3.
View Answer
(10×2 + 30×3)/(2+3) = (20 + 90)/5 = 110/5 = 22
22
Q5. A mixture of 50 L milk is replaced twice with 10 L water each time. Find milk left.
View Answer
50(1 - 10/50)^2 = 50(0.8)^2 = 50×0.64 = 32
32 L milk
Q6. The average age of 5 students is 16. When a new student joins, average becomes 17. Find the age of new student.
View Answer
(17×6) - (16×5) = 102 - 80 = 22
22 years
8. Quick Summary Table
| Concept | Formula | Tip |
|---|---|---|
| Average | Sum ÷ Count | No units |
| Weighted Avg | Σwx / Σw | Unequal weights |
| Replacement | V(1 - x/V)^n | Used in mixtures |
| Added/Removed | (New Avg - Old Avg) × Total | Fast trick |
| Consecutive Nos. | (First + Last)/2 | Always middle value |
You've completed Article 6: Average!
Courage Tip: In SSC exams, average questions are often linked — e.g., "average of first half & second half," "replacement in mixture," or "average speed." Always check the base formula before jumping to tricks.
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