Question

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

Answer 1

Let present age of Hari be 5M and present age of Harry be 7M.

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

After 4 years

Age of Hari = (5M + 4) years

And age of Harry = (7M + 4) years

• A.T.Q.

=> $\dfrac{5M\:+\:4}{7M\:+\:4}$ = $\dfrac{3}{4}$

• Cross-multiply them

=> 4(5M + 4) = 3(7M + 4)

=> 20M + 16 = 21M + 12

=> 20M - 21M = 12 - 16

=> 20M - 21M = - 4

=> - M = - 4

=> M = 4

_____________________________

Present age of Hari = 5M = 5(4) = 20 years

Present age of Harry = 7M = 7(4) = 28 years

_______________[ANSWER]

Answer 2

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

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

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

Given :

Ages of Hari and Harry = 5 : 7

Ages after 4 years = 3 : 4

To Find :

Their present Ages

Solution :

Consider the age of Hari as 5x and Harry as 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

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

$\sf{\implies} \:20$

Hari is 20 years old.

★ Value of 7x

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

$\sf{\implies} \:28$

Harry is 28 years old.

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

$\rule{300}{1.5}$

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

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

$\sf{\implies} \:{\dfrac{20+ 4}{28 + 4} = \dfrac{3}{4}}$

$\sf{\implies} \:{\dfrac{24}{32} = \dfrac{3}{4}}$

$\sf{\implies} \:{\dfrac{24 \div 8}{32 \div 8} = \dfrac{3}{4}}$

$\sf{\implies} \:{\dfrac{3}{4} = \dfrac{3}{4}}$

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