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 youngest new member?
Show answer & explanation
Correct answer: D
Explanation
Correct Answer is option 4 i.e.10
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Concept |
Understanding |
Application |
Fair calculation |
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Average |
Average age of family of 5 members 9 years ago = 33 years Suppose The age of new members be x, (x + 8) and (x + 16) |
Total age of 5 members 9 years ago = 33 × 5 = 165 Hence, Total age of 5 members at present = 165 + 5 × 9 = 210 Since present average is same as 33 years after adding 3 new members: ⇒ [210 + x + x + 8 + x + 16]/8 = 33 ⇒ x = 10 Hence, age of youngest new member = 10 years |
⇒ [210 + x + x + 8 + x + 16]/8 = 33 ⇒ [234 + 3x] = 33 × 8 ⇒ [234 + 3x] = 264 ⇒ 3x = 264 – 234 = 30 ⇒ x = 10 |