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- Quantitative Aptitude
The average age of Donald, his wife and their two children is $23\, years.$ His wife is just $4 \,year$ younger than Donald himself andxhis wife was $24\, years$ old when his daughter was born. He was $32 \,years$ old when his son was born. Th average age of Donald and his daughter is ? (in $year$)
$25$
$22.5$
$26$
$23$
Solution
Let Donald be denoted by $H$ (Husband)
His wife be denoted by $W$, His daughter be denoted by $D$, His son be denoted by $S$
The average age of $4$ persons
$=\frac{H+W+D+S}{4}=23$
$H + W + D + S =92 \Rightarrow H = W +4$
| $H$ | $W$ | $D$ | $S$ | ||
| At the time when daughter is born $\rightarrow$ | $28$ | $\xleftarrow{{\left({+4}\right)}}$ | $24$ | $0$ | $X$ |
| $\downarrow$ | |||||
| At the time when Son is born$\rightarrow$ | $32$ | $\xleftarrow{{\left({-4}\right)}}$ | $28$ | $4$ | $0$ |
So at the time of birth of his Son, total age of his family $=64$ $years.$ $(32+28+4+0=64)$ and presently the total age of his family $=92$ $years.$ It means total increase in age of the whole family $=28$ $years.$
Thus average increase in age $=\frac{28}{4}=7$ $years.$
It means the age of Donald $=39$ $years$ and age of his daughter $=11$ years Therefore the average age of Donald and his Daughter is $25\, years.$
