Average age of six people six years ago was 42 years. Now if the seventh person joins the group average becomes 46 years. Find the age of seventh person after seven more years.
Answers
- The age of seventh person after seven more years is equal to 41 years .
Given :-
- Average age of six people six years ago was 42 years .
- if the seventh person joins the group average becomes 46 years .
To Find :-
- The age of seventh person after seven more years ?
Formula used :-
- Average = Sum of all observations / Total number of observations .
Solution :-
given that,
→ Total people = 6
→ Average of all 6 people six years ago = 42
So,
→ Sum of ages of all 6 people six years ago = Average at that time × Total people = 42 × 6 = 252 years
now,
→ Sum of ages of all 6 people six years ago = 252
then,
→ Total ages of all 6 people at present = 252 + years × number of people = 252 + 6 × 6 = 252 + 36 = 288 years .
Now, let us assume that, the present age of seventh person is equal to x years .
So,
→ Total people = 6 + 1 = 7
→ New average = 46
→ Total ages of all 7 people now = Total ages of all 6 people + Present age of seventh people = (288 + x) years .
therefore,
→ New average = Total ages of all 7 people / Total people
→ 46 = (288 + x)/7
→ 46 × 7 = 288 + x
→ 322 = 288 + x
→ x = 322 - 288
→ x = 34 years.
hence,
→ The age of seventh person after seven more years = Present age of seventh person + 7 = x + 7 = 34 + 7 = 41 years (Ans.)
Hence, the age of seventh person after seven more years is equal to 41 years .
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