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Averages · Topic 4 of 6

🔄 Join, Leave & Replace

2 exam question types, fully solved

These are the most common average questions in SSC: a person joins, leaves, or is replaced, and the average shifts a little. One idea solves them all — a change in the average is felt by every member.

One shortcut for the whole family

When the average moves, multiply that move by the number of people to see the total weight/marks/age that came in or went out:

• Replacement (one swaps for one): the count stays the SAME. The person leaving is the “old value”; add for an increase, subtract for a fall. A weight dropping by 3 for 12 people means a swing of .

• Joining (count rises by 1): build totals — new total — and subtract the old total to get the newcomer. The new person must cover their own share of the average AND lift everyone else.

• A whole group merging in: combined average . To find a missing count, set total surplus (final strength) (rise per head).

Direction check: average up ⇒ the newcomer is above the old average; average down ⇒ below it.

📊Average Builderinteractive
avg = 5.4
4
7
2
9
5
Sum (S)
27
Count (N)
5
Average
5.4
Average = 27 ÷ 5 = 5.4

9 members average 32; a 10th joins and the average becomes 34. The newcomer is .

📝Practice Questions

Q1The average of 5 numbers is 40. A 6th number is added and the average becomes 42. The 6th number is:

Q2In a class of 30, the average mark rises by 1.5 when one student scoring 50 is replaced. The new student scored:

Q3A group of 10 averages 30; another group of 5 averages 20. The combined average is:

📚

Real exam questions — Join, Leave & Replace

2 question types · 8 solved examples from real SSC papers

One shortcut runs the whole family: New value = Old value + (count × change in average). Replacement keeps the count; joining raises it by one.

How to solve this type
The whole family runs on one shortcut, the “change spreads to everyone” idea:
New value=Old value+(count×change in average)\text{New value} = \text{Old value} + (\text{count} \times \text{change in average})
Replacement (one swaps for one): the count stays the SAME. The person who leaves is the old value; add count × (rise in average), or subtract count × (fall).
Joining (count goes up by 1): build totals — new total == new count × new average — and subtract the old total to get the newcomer.
Golden rule: a rise in average means the newcomer is above the old average; a fall means below.

The average age of 9 members is 32 years. A new member joins and the average becomes 34. Find the new member's age.

A52B48C50D54

The average weight of 12 persons decreases by 3 kg when a person weighing 72 kg is replaced. Find the new person's weight.

A36B40C34D38

The average weight of 15 people increases by 3.2 kg when a new person replaces one weighing 52 kg. Find the new person's weight.

A104B100C96D108

The average weight of 30 students is 60 kg. When the class teacher is included, the average rises by 0.5 kg. Find the teacher's weight.

A76B74.5C75D75.5