Mr. Sharma’s family consists of 6 people. Mr Sharma, Mrs. Sharma and four Son’s. Average age of the family immediately after the birth of 1st, 2nd, 3rd and 4th son was 16, 15, 16 and 15 years respectively. Find the age of eldest son if the present average age of the entire family is 16 years.
Explanation:
Sum of the ages immediately after the birth of 1st child = 16 × 3 = 48
Sum of the ages immediately after the birth of 2nd child = 15 × 4 = 60
The difference between the sum of the ages = 60 – 48 = 12 is due to 3 persons growing by same number of years. Hence, the gap between birth of 1st child and 2nd child = 12/3 = 4 years.
Similarly, the difference between the birth of 2nd and 3rd child = (16 × 5 – 15 × 4)/4 = 5 years
Similarly, the difference between the birth of 3rd child and 4th child = (15 × 6 – 16 × 5)/5 = 2 years
Hence, when the 4th child was born, the 1st child would be = 4 + 5 + 2 = 11 years old.
When 4th child was born the average age of the family was 15 years and current average age is 16 which implies that each of the family member grows 1 year. Hence, the current age of the 1st child = 11 + 1 = 12 years
Hence, option (b).
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