Question

the age of aman and priya arein the ratio 5:7 . four years later from now the ratio of their ages will be 3:4 . find the present ages.​

Answer 1

$\overline{\underline{\boxed{\sf GIVEN \darr}}}$

• The ages of aman and priya are in the ratio 5 : 7

• Four years later from now the ratio of their ages will be 3 : 4

• Find the present ages

$\overline{\underline{\boxed{\sf SOLUTION \darr}}}$

Let the constant multiple be x

The ratio of their present ages :

Aman's age = 5x

Priya's age = 7x

After 4 years :

Aman's age = 5x + 4

Priya's age = 7x + 4

After 4 years the ratio of their ages is :

Aman's age = 3

Priya's age = 4

Henceforth, the equation is :

$\sf \mapsto \frac{5x + 4}{7x + 4} = \frac{3}{4}$

By cross multiplying we get

$\sf \mapsto4(5x + 4) = 3(7x + 4)$

By further simplifying we

$\sf \mapsto20x + 16 = 21x + 12$

$\sf \mapsto21x - 20x = 16 - 12$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star \: \green{{\underline{\boxed{ \red{\sf x = 4 }}}}}\sf$

___________________________________________

Present age ratio :

Aman's = 5x

Priya's = 7x

Therefore,

$\star \: \green{{\underline{\boxed{ \red{\frak{Aman's \: age= 5 × 4 = 20\: years }}}}}}\sf$

$\star \: \green{{\underline{\boxed{ \red{\frak{Priya's \: age= 7 × 4 = 28 \: years }}}}}}\sf$

Answer 2

Answer :

$\small{ \green{ \boxed{ \dag\bf \: present \: age \: of \: \: aman \: = 20 \: years}}} \\ \\ \small{ \orange{ \boxed{ \dag\bf \: present \: age \: of \: priya \: \: = 28 \: years}}}$

Given:

★ The ratio of present ages of Aman and Priya

= 5 : 7

★ After four years ratio of ages of Aman and Priya = 3:4

To find:

The present ages of Aman and Priya.

Solution:

→ Let the ages of Aman and Priya be 5x and 7x

respectively.

→ After 4 years the age of Aman will be = 5x+4

And

→ After 4 years the age of Priya will be = 7x+4

Therefore,

According to the question,

$\: \: \: \: \: \: \: \: \bf \frac{5x + 4}{7x + 4} = \frac{3}{4}\\ \\ \bf \implies \: 4(5x + 4) = 3(7x + 4) \\ \\ \bf \implies \: 20x + 16 = 21x + 12 \\ \\ \bf \implies \:21x - 20x = 16 - 12 \\ \\ \bf \implies \: x = 4 \\ \\ \bf \therefore \: x = 4 \\ \\ \sf \: now \\ \small{ \pink{\bf \: present \: age \: of \: \: aman \: = 5x = 5 \times 4 = 20 \: years}} \\ \\ \small{ \pink{\bf \: present \: age \: of \: priya \: \: = 7x = 7 \times 4 = 28 \: years}}$