Question

The ages of Sona and Mona are in the ratio 5:3. Five years later, the ratio of their ages will be 10:7. Find their

ages after 10 years.​

Answer 1

Given :

Present ages' ratio : 5:3

Ratio of 5 years later : 10:7

To find :

The ages of Sona and Mona after 10 years.

Solution :

First, we should find the present ages of Sona and Mona.

According to the question,

$\sf \dashrightarrow 5:3 = 10:7$ (5 years later)

$\sf \dashrightarrow \dfrac{5x + 5}{3x + 5} = \dfrac{10}{7}$

$\sf \dashrightarrow 7(5x + 5) = 10(3x + 5)$

$\sf \dashrightarrow 35x + 35 = 30x + 50$

$\sf \dashrightarrow 35x - 30x = 50 - 35$

$\sf \dashrightarrow 5x = 15$

$\sf \dashrightarrow x = \dfrac{15}{5}$

$\sf \dashrightarrow x = 3$

Now, we should find the present ages of Sona and Mona.

Present age of Sona :

$\sf \dashrightarrow 5x = 5(3)$

$\sf \dashrightarrow 15 \: years$

Present age of Mona :

$\sf \dashrightarrow 3x = 3(3)$

$\sf \dashrightarrow 9 \: years$

Now, we can find the ages of them, after 10 years.

Age of Sona (10 years later) :

$\sf \dashrightarrow 15 + 10$

$\sf \dashrightarrow 25 \: years$

Age of Mona (10 years later) :

$\sf \dashrightarrow 9 + 10$

$\sf \dashrightarrow 19 \: years$

Hence, the ages of Sona and Mona, 10 years later is 25 and 19 years.