Question 67

9 years ago, the average age of a family of five members was 33 years. Now, three new members join whose ages are in ascending order with consecutive gaps of 8 years. If the present average age of the family is the same as it was 9 years ago, what is the age (in years) of the eldest new member?

Solution

Let the sum of ages of 5 persons 9 years ago be S 
so we get S = 33(5) = 165 
Now sum of present ages of the 5 members = 165 +5(9) = 165+45 =210
Now let the ages of the three new members be a-8 , a and a+8 years 
Now we can say the present average age of family is given as : 33 years
Also the number of members in the family are : 8
Therefore we can say the sum of present ages of 8 members of the family will be :
33(8) = 264 = 210+a-8+a+a+8
so we get 54 =3a
a=18 years
Now therefore the age of the eldest member will be : 18+8 =26 years


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