Question

The present ages of A & B are in the ratio of 7:5. Ten years later, the ratio will change to 9:7. Find their present ages

Answer 1

Ratio of the present ages of Sonu and Monu = 7:5
Let the ages be 7x and 5x
Ages after 10 years = (7x + 10) and (5x + 10)
Ratio of ages after 10 years = 9:7
⇒ (7x + 10) : (5x + 10) = 9 : 7
Product of extremes = Product of means
7(7x + 10) = 9(5x + 10)
49x + 70 = 45x + 90
49x - 45x = 90 - 70
4x = 20
x = 5
Therefore, the present ages of Sonu and Monu are (7x5) and (5x5) i.e. 35 years and 25 years.





Hope it helps.....:)

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