Average age of ten persons learning yoga is 32 years. When the age of their instructor is added, the average age becomes 34 years. The age of their instructor is

### Concept & Strategy When a new person joins a group and the average increases, the new person's value must be greater than the old average. Their age covers the original average PLUS the total increase distributed among all members (including themselves). $$Total = Average \times Number of Entities$$ ### Step-by-Step Solution * **Calculate the initial total age:** For 10 persons with an average of 32 years: $$Sum_{initial} = 10 \times 32 = 320 \text{ years}$$ * **Calculate the new total age:** When the instructor joins, there are 11 people. The new average is 34 years: $$Sum_{new} = 11 \times 34 = 374 \text{ years}$$ * **Find the instructor's age:** Subtract the initial total from the new total: $$Instructor = 374 - 320 = 54 \text{ years}$$ ### Exam Strategy & Shortcut Use the "Deviation Method" for a lightning-fast mental calculation. The instructor brings enough age to be exactly the old average (32), plus enough extra age to increase all 11 people's averages by 2 years ($34 - 32$). $$Age = \text{Old Average} + (\text{Total New Members} \times \text{Increase in Average})$$ $$Age = 32 + (11 \times 2) = 32 + 22 = 54$$ ### Common Pitfall Multiplying the increase in average by the *old* number of members (10) instead of the *new* number of members (11). The instructor also needs those 2 extra years to bring their own base age of 32 up to 34. ### Final Answer **Therefore, the correct answer is 54 years.**