Question

present ages of soham and soha are in the ratio 7:12. if two years ago the ratio of their ages was 3:8 then their present ages are​

Answer 1

Let present age of sonam be 7x

present age of soha = 12x

Two years age

Sonam age = 7x - 2

Soha age = 12x - 2

A/Q

$7x - 2 \: \ratio \: 12x - 2 = 3 \: \ratio \: 8 \\ = > \frac{7x - 2}{12x - 2} = \frac{3}{8} \\ = > 8(7x - 2) = 3(12x - 2) \\ = > 56x - 16 = 36x - 6 \\ = > 56x - 36x = 16 - 6 \\ = > 20x = 10 \\ = > x = \frac{10}{20} \\ = > x = \frac{1}{2}$

Answer 2

Solution -

Firstly, let the ratio of their ages be x. Then,

⇢ Soham's present age = 7x

⇢ Soha's present age = 12x

⠀

Two years ago

⇢ Soham's age = (7x - 2)

⇢ Soha's age = (12 - 2)

⠀

It is given that two years ago the ratio of their ages was 3:8.

⠀

According to the question

$\tt:\implies\: \: \: \: \: \: \: \: {\dfrac{(7x - 2)}{(12x - 2)} = \dfrac{3}{8}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {8(7x - 2) = 3(12x - 2)}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {56x - 16 = 36x - 6}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {56x - 36x = - 6 + 16}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {20x = 10}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{10}{20}}$

⠀

$\bf:\implies\: \: \: \: \: \: \: \: {x = \dfrac{1}{2}}$

⠀

By putting the value of x

➝ Soham's present age = $\sf{\dfrac{7}{2} = 3.5}$

➝ Soha's present age = $\sf{\dfrac{12}{2} = 6}$

⠀

Hence,

• Present age of Soham is 3.5 years.
• Present age of Soha is 6 years.

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