| 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 \[5\frac{1}{2}\text{yr},\] then find the age of the father and the mother. |
A) 37 yr and 28 yr
B) 47 yr and 38 yr
C) 50 yr and 41 yr
D) 35 yr and 32 yr
Correct Answer: A
Solution :
| Let the age of father and mother be x yr and y yr, respectively. |
| Total age of the four members \[=19\times 4=76\,\,yr\] |
| Total age of two boys \[=\frac{11}{2}\times 2=11\,\,yr\] |
| 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 |
| \[x=37\,\,yr\]and \[y=28\,\,yr\] |
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