PREVIOUSLY ASKED IN:
PSC Miscellaneous Prelims 2018
Answer
65
Explanation
According to the rule of averages, Total Sum = Average × Number of items. Given, the average of 5 numbers is 50. Therefore, the sum of all 5 numbers = 5 × 50 = 250. It is also given that the average of 3 of these numbers is 40. Therefore, the sum of these 3 numbers = 3 × 40 = 120. The sum of the remaining 2 numbers will be = (Total sum of 5) - (Sum of 3) = 250 - 120 = 130. Since there are 2 remaining numbers, their average is = 130 ÷ 2 = 65.
Key Points
- > Primary formula for average: Average = Sum of all terms / Total number of terms.
- > Derived formula for sum: Sum = Average × Total number of terms.
- > Total sum of the 5 numbers = 5 × 50 = 250.
- > Sum of the 3 specified numbers = 3 × 40 = 120.
- > Sum of the remaining 2 numbers = 250 - 120 = 130.
- > Average of these 2 numbers = 130 / 2 = 65.
Additional Information
Table for Solving Average Problems
| Number of Items | Average | Total Sum (Items × Average) |
|---|---|---|
| 5 Numbers | 50 | 250 |
| 3 Numbers | 40 | 120 |
| Remaining 2 | ? | 250 - 120 = 130 |
| Final Average | 65 | 130 ÷ 2 = 65 |
Memory Tips
- Deviation Trick: The overall average is 50. The 3 numbers have an average of 40, which is a deviation of -10 each (total deviation = -30). To balance this, the remaining 2 numbers must have a positive deviation of +30 combined. That means +15 for each of the two numbers. So their average is 50 + 15 = 65.