The average age of a group of 5 men is 30 years. If a new man joins the group, the average age becomes 32 years. What is the age of the new man?

Question

Accepted Answer

Average problems can be solved quickly by tracking the total sum of observations.

### Formula:
$$	ext{Average} = \frac{	ext{Sum of Observations}}{	ext{Number of Observations}}$$

### Step-by-Step Solution:
1. **Calculate the total age of the initial 5 men:**
   $$	ext{Sum}_5 = 	ext{Average}_5 	imes 5 = 30 	imes 5 = 150 	ext{ years}$$
2. **Calculate the total age of the 6 men (including the new member):**
   $$	ext{Sum}_6 = 	ext{Average}_6 	imes 6 = 32 	imes 6 = 192 	ext{ years}$$
3. **Find the age of the new man:**
   $$	ext{Age of new man} = 	ext{Sum}_6 - 	ext{Sum}_5$$
   $$	ext{Age} = 192 - 150 = 42 	ext{ years}$$

**Answer:** The age of the new man is **42 years**.

The average age of a group of 5 men is 30 years. If a new man joins the group, the average age becomes 32 years. What is the age of the new man? - DDCET Q&A

The average age of a group of 5 men is 30 years. If a new man joins the group, the average age becomes 32 years. What is the age of the new man?

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