Question

the age of Rakesh and Dinesh are in the ratio 5 ratio 7 after 5 years the ratio of their age will be 5 ratio 6 find their present age​

Answer 1

Answer:

The present ages of Rakesh and Dinesh are 5 years and 7 years respectively.

Step-by-step explanation:

Given :

Present age Ratio = 5 : 7

Ratio is ages after 5 years = 5 : 6

To find :

Their present ages

Solution :

Let their present ages be -

• Rakesh as 5y
• Dinesh as 7y

Ages after 5 years -

• Rakesh = (5y + 5)
• Dinesh = (7y + 5)

$\sf{\longrightarrow} \: \dfrac{5y + 5}{7y + 5} = \dfrac{5}{6} \\ \\ \sf{\longrightarrow} \: 6(5y + 5) = 5(7y + 5) \\ \\ \sf{\longrightarrow} \: 30y + 30 = 35y + 25 \\ \\ \sf{\longrightarrow} \: 35y - 30y = 30 - 25 \\ \\ \sf{\longrightarrow} \: 5y = 5 \\ \\ \sf{\longrightarrow} \: y = 1$

$\rule{300}{1.5}$

★ Rakesh's present age -

$\sf{\longrightarrow} \: 5(1) \\ \\ \sf{\longrightarrow} \: 5$

Rakesh is 5 years old.

$\rule{300}{1.5}$

★ Dinesh's present age -

$\sf{\longrightarrow} \: 7(1) \\ \\ \sf{\longrightarrow} \: 7$

Dinesh is 7 years old.

$\therefore$ The present ages of Rakesh and Dinesh are 5 years and 7 years respectively.

Answer 2

Answer:

${\underline{\underline{\sf\red{Answer :- }}}}$

$\diamond\sf Present \: age \: of \: Rakesh ={\boxed{\sf\green{5 \: years}}}$

$\diamond\sf Present \: age \: of \: Dinesh ={\boxed{\sf\blue{7 \: years }}}$

${\underline{\underline{\sf\blue{Explanation:- }}}}$

Given:-

• Present age ratio = 5 : 7
• After 5 years,ratio = 5 : 6

To find:-

• Present ages = ?

Let present ages of Rakesh and Dinesh be 5x & 7x years.

After 5 years,

$\dashrightarrow\sf Age \: of \: Rakesh = (5x + 5)\: years$

$\dashrightarrow\sf Age \: of \: Dinesh = (7x + 5)\: years$

${\underline{\underline{\sf\green{ATQ:- }}}}$

$\dashrightarrow\sf (5x + 5) : (7x + 5) = 5 : 6 \\\\\dashrightarrow\sf \dfrac{(5x + 5)}{(7x + 5)} =\dfrac{5}{6} \\\\\dashrightarrow\sf 5(7x + 5) = 6(5x + 5) \\\\\dashrightarrow\sf 35x + 25 = 30x + 30 \\\\\dashrightarrow\sf 35x - 30x = 30 - 25 \\\\\dashrightarrow\sf 5x = 5 \\\\\dashrightarrow\sf x = 5/5 \\\\\dashrightarrow\sf x =\large{\boxed{\sf\red{1 \: year}}}$

$\rule{200}{1}$

$\dashrightarrow\sf Age \: of \: Rakesh = 5x= 5(1) =\large{\boxed{\sf\blue{5\: years}}}$

$\dashrightarrow\sf Age \: of \: Dinesh =7x = 7(1) = \large{\boxed{\sf\blue{7 \: years }}}$

$\therefore\sf Present \: age \: of \: Rakesh = 5 \: years$

$\therefore\sf Present \: age \: of \: Dinesh = 7 \: years$