Question

The ages of sona and sonli are in the ratio 5:3. Five years hence, the ratio of their ages will be 10:7. Find their present ages

Answer 1

Ratio of Present Age of Sona and Sonli=5:3.

Let Present Age of Sona=5x years

Let Present age of Sonli=3x years.

After 5 years

Sona Age will be=(5x+5) years

Sonli age will be=(3x+5) years

Now Their Ratio will be=10:7

As we know

$x:y = \frac{x}{y} </p><p>$

So,

$\frac{5x + 5}{3x + 5} = \frac{10}{7} \\ \\ 7(5x + 5) = 10(3x + 5) \\ \\ 35x + 35 = 30x + 50 \\ \\ 35x - 30x = 50 - 35 \\ \\ 5x = 15 \\ \\ x = \frac{15}{5} \\ \\ x = 3$

Present age of Sona=5x=5×3=15 years

Present age of Sonli=3x=3×3=9 years

Sona=15 years

Sonli=9 years

Answer 2

• A.T.Q.

The ages of Sona and Sonali are in the 5:3.

Let age of Sona be 5x.

And

Age of Sonali be 3x.

Five years hence (after means sum), the ratio of their (Sona and Sonali) ages will be 10:7.

$\implies$ $\dfrac{5x\:+\:5}{3x\:+\:3}$ = $\dfrac{10}{7}$

Cross-multiply them

$\implies$ 7(5x + 5) = 10(3x + 5)

$\implies$ 35x + 35 = 30x + 50

$\implies$ 35x - 30x = 50 - 35

$\implies$ 5x = 15

$\implies$ x = $\dfrac{15}{5}$

$\implies</strong><strong>$ x = 3

• So, Present age of Sona = 5x = 5(3) = 15 years.

And

• Present age of Sonali = 3x = 3(3) = 9 years.