Question

The ages of hari and Harry are in the ratio 5:7. Four year from now the ratio of their ages will be 3:4. Find their present ages. ​

Answer 1

Answer:

$\large{\underline{\boxed{\sf Hari's \: age = 20 \: years}}}$

$\large{\underline{\boxed{\sf Harry's \: age = 28 \: years}}}$

Step-by-step explanation:

Let the age of Hari and Harry be 5x and 7x respectively.

Four years from now:

Hari's age = 5x + 4

Harry's age = 7x + 4

The ratio will be 3:4.

Equation formed;

$\sf \frac{5x + 4}{7x + 4} = \frac{3}{4} \\ \\ \bf on \: cross - multiplying : \\ \\ \implies \sf 3(7x + 4) = 4(5x + 4) \\ \\ \implies \sf 21x + 12 = 20x + 16 \\ \\ \implies \sf 21x - 20x = 16 - 12 \\ \\ \implies \sf x = 4$

_______________________

★ Age of Hari-

⇒ 5x

⇒ 5 * 4

⇒ 20 years

★ Age of Harry-

⇒ 7x

⇒ 7 * 4

⇒ 28

_______________________

Hence, the present age of Hari and Harry is 20 years and 28 years.

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

Hari is presently 20 years old and Harry is 28 years old

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Ages of Hari and Harry in ratio = 5 : 7

4 years from now the ratio = 3 : 4

To Find :

Their present ages

Solution :

Consider their present ages as

• Hari's age 5x
• Harry's age 7x

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

$\sf{\implies}\:\dfrac{5x + 4}{7x + 4} =\dfrac{3}{4}$

$\sf{\implies}\:4(5x + 4) = 3(7x + 4)$

$\sf{\implies}\:20x + 16 = 21x + 12$

$\sf{\implies}\:21x - 20x = 16 - 12$

$\sf{\implies}\:x =4$

$\rule{300}{1.5}$

★ Value of 5x

$\sf{\implies} \:5 \times 4$

$\sf{\implies} \:20$

★ Value of 7x

$\sf{\implies} \:7 \times 4$

$\sf{\implies} \:28$

Hari is 20 years old

Harry is 28 years old

$\rule{300}{1.5}$

$\therefore$ Hari is presently 20 years old and Harry is 28 years old.