Question

# A and B are friends. A is elder to B by 5 years. B's sister C is half the age of B while A's father D is 8 years older than twice the age of B. If the present age of D is 48 years, they find the present ages of A, B and C.

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Solution

## $\mathrm{Let}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{B}\mathrm{be}x\mathrm{yrs}.\mathrm{Then},\phantom{\rule{0ex}{0ex}}\mathrm{The}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{A}=\left(x+5\right)\mathrm{yrs},\phantom{\rule{0ex}{0ex}}\mathrm{The}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{C}=\frac{x}{2}\mathrm{yrs}\mathrm{and}\phantom{\rule{0ex}{0ex}}\mathrm{The}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{D}=\left(2x+8\right)\mathrm{yrs}\phantom{\rule{0ex}{0ex}}\mathrm{But}\mathrm{the}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{D}=48\mathrm{yrs}\phantom{\rule{0ex}{0ex}}⇒2x+8=48\phantom{\rule{0ex}{0ex}}⇒2x=48-8\phantom{\rule{0ex}{0ex}}⇒2x=40\phantom{\rule{0ex}{0ex}}⇒x=\frac{40}{2}\phantom{\rule{0ex}{0ex}}⇒x=20\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{So},\phantom{\rule{0ex}{0ex}}\mathrm{The}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{A}=20+5=25\mathrm{years},\phantom{\rule{0ex}{0ex}}\mathrm{The}\mathrm{present}\mathrm{age}\mathrm{of}\mathrm{B}=20\mathrm{years}\mathrm{and}\phantom{\rule{0ex}{0ex}}\mathrm{The}\mathrm{present}\mathrm{of}\mathrm{C}=\frac{20}{2}=10\mathrm{years}$

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