Quantitative Aptitude Ques 1296

Question: The average age of two boys and their father is greater than the average age of those two boys and their mother by 3 yr. The average age of the four is 19 yr. If the average age of the two boys be $ 5\frac{1}{2}yr, $ then find the age of the father and the mother.

Options:

A) 37 yr and 28 yr

B) 47 yr and 38 yr

C) 50 yr and 41 yr

D) 35 yr and 32 yr

Show Answer

Answer:

Correct Answer: A

Solution:

  • Let the age of father and mother be x yr and y yr, respectively. Total age of the four members $ =19\times 4=76yr $ Total age of two boys $ =\frac{11}{2}\times 2=11yr $ According to the question, $ \frac{11+x}{3}=\frac{11+y}{3}+3 $

$ \Rightarrow $ $ 11+x=11+y+9 $

$ \Rightarrow $ $ x-y=9 $ … (i)

$ \Rightarrow $ $ x+y+11=76 $
$ \Rightarrow $ $ x+y=76-11 $

$ \Rightarrow $ $ x+y=65 $ … (ii) On solving Eqs. (i) and (ii), we get $ x=37yr $ and $ y=28yr $

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