6. The ages of Hari 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.

Let the present ages of Hari=5x and Harry=7x years.
After 4 years Hari’s age will be (5x + 4) years and Harry’s age will be (7x + 4) years.

As per the conditions given, we have

\(\frac { 5x+4 }{ 7x+4 } =\frac { 3 }{ 4 }\)

\(\Rightarrow 4(5x + 4) = 3(7x + 4)\quad\) [Cross-multiplication]

\(\Rightarrow 20x + 16 = 21x + 12\quad \) [Solving the bracket]

\(\Rightarrow 20x – 21x = 12 – 16 \quad \)[Transposing 21x to LHS and 16 to RHS]

\(\Rightarrow -x = -4\)

\(\Rightarrow x = 4\)

Hence, the present ages of Hari and Harry are 5 × 4 = 20years and 7 × 4 = 28years respectively.