Question

When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 added instead, the average age decreases by 1. The value of n is

• A. 7

Answer 1

The correct option is A 7
The initial average must have been between 39 and 15. When a person aged 39 is added to the group, the average increases and when a person aged is 15 is added, the average decreases. Let's look at the second case first. When the person aged 15 is added, the average becomes (initial average 1).
If instead, the person aged 39 were added to the group, there would be 39-15=24 extra which would make the average = (initial average +2).
This differences of 24 creates a differences of 3 in the average.
This means there must have been $\frac{24}{3}$=8 people (after adding the extra person).
The value of n must be 8-1=7