FAQs on Tricks to solve problems based on Including/Excluding concept of Average

Question 1

1. How do I quickly find the new average when one person is added or removed from a group?

Accepted Answer

Ans. The including/excluding concept uses a simple formula: multiply the original average by the total count to find the sum, then add or subtract the new/removed value and divide by the new total. For example, if 5 people average 60 marks and one person scoring 80 joins, the new average becomes (5×60 + 80)÷6 = 70. This trick saves time by avoiding recalculation from scratch.

Question 2

2. What's the difference between problems where someone is replaced versus added in average questions?

Accepted Answer

Ans. In replacement problems, the total count stays the same-only the sum changes. When someone is added or excluded, both the sum and count change. For replacement, use: New Average = Old Average + (New Value - Old Value)÷Count. For inclusion/exclusion, recalculate the denominator. Recognizing this distinction prevents calculation errors during CLAT exams.

Question 3

3. Why do students get confused between net change and absolute change in average problems?

Accepted Answer

Ans. Net change refers to the difference in total sum caused by addition or removal, while absolute change measures the shift in average itself. A person scoring 20 more than the average increases the net sum but may only raise the average slightly due to the increased denominator. Understanding this distinction clarifies why averages don't shift proportionally to individual scores.

Question 4

4. Can I solve including/excluding average problems without writing out all the calculations?

Accepted Answer

Ans. Yes-use the deviation method. Find how much each new or removed value deviates from the original average, then calculate its impact on the new average directly: Change in Average = (Deviation)÷(New Total Count). This mental shortcut works for CLAT questions where speed matters, avoiding lengthy arithmetic while maintaining accuracy.

Question 5

5. What tricks help when multiple people are added or removed from a group's average?

Accepted Answer

Ans. Calculate the combined sum of all added/removed individuals, then apply it as one adjustment: New Average = (Old Sum ± Combined Adjustment)÷(New Count). For instance, if two people scoring 70 and 80 join a group of 10 averaging 60, the new average is (600 + 150)÷12 = 62.5. This batching method reduces errors in multi-person problems.

Tricks to solve problems based on Including/Excluding concept of Average

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