Question

The present ages of A and B are in the ratio 7:5.Ten years later, their ages will be
in the ratio 9:7. Find their present ages.​

Answer 1

Let the Present age of A = 7x years.

The Present age of B = 5 x years.

After 10 years their age will be

A = 7x + 10 years.

B = 5x + 10 years.

The ratio of the ages after 10 years 9 : 7

⟹ $\frac{7x+10}{5x+10}$ = $\frac{9}{7}$

⟹ 49x + 70 = 5x +90

⟹ 49x - 45x = 90 - 70

⟹ 4x = 20

⟹ x = 5

Present age of A = 7 × 5 = 35 Years.

Present age of B = 5 × 5 = 25 Years.

Answer 2

$\huge \blue\star \: \pink{ \underline { \textbf{\textsf{Solution :- }}}}$

Let the present age of A = 7x years

The present age Of B = 5x years

After 10 years, their ages will be

A = 7x + 10 years

B = 5x + 10 years

The ratio of the ages after 10 years 9 : 7

$\implies\large \frac{7x + 10}{5x + 10} = \frac{9}{7}$

${\implies49x + 70 = 5x + 90}$

${\implies49x - 45x = 90 - 70}$

${\implies4x = 20}$

${\implies x = 5}$

Present age of A = 7 × 5 = 35 Years

Present Age of B = 5 × 5 = 25 Years