Question

The ages of Han and Harry are in the ratio $5:7$. Four years from now, the ratio of their ages will be $3:4$. Find their present ages.

• A. Present age of Han $=15$years
  Present age of Harry $=21$years
• B. Present age of Han $=25$years
  Present age of Harry $=35$years
• C. Present age of Han $=20$ years
  Present age of Harry $=28$years
• D. Present age of Han $=25$years
  Present age of Harry $=30$years

Answer 1

Answer: (C)

Present age of Han $=20$ years

Present age of Harry $=28$years
Let the present ages of Han and Harry be $5x$ years and $7x$ years respectively.

After $4$ years,
Han's age $=(5x+4)$ years
Harry's age $=(7x+4)$ years
$\therefore \frac{5x+4}{7x+4}=\frac{3}{4}$ ....(Given)
$\Rightarrow 4(5x+4)=3(7x+4)$ ....[By cross-multiplication]
$\Rightarrow 20x+16=21x+12$
$\Rightarrow 20x-21x=12-16$ ....[Transposing $21x$ to LHS and 16 to RHS]
$\Rightarrow -x=-4$, i.e., $x=4$
$\therefore$ Present age of Han $=5\times 4$ years $=20$ years
and present age of Harry $=7\times 4$ years $=28$ years.