Question

the ratio of present ages of albert and salim is 5:9.five years hence ratio of their ages will be 3:5.find their present ages​

Answer 1

Answer:

Albert is 25 years old.

Salim is 45 years old.

Step-by-step explanation:

Albert's present age ➝ 5x.

Salim's present age ➝ 9x.

[Since the ages are in the form of a ratio, we've multiplied the ratio with 'x' where 'x' is a constant]

Five years later, Albert's and Salim's age will be:

• Albert's age 5 years later ➝ 5x + 5

• Salim's age 5 years later ➝ 9x + 5

The ratio of Albert's and Salim's age 5 years later is 3:5.

Therefore:

$\sf \Longrightarrow \dfrac{Albert's \ age \ 5 \ years \ later}{Salim's \ age \ 5 \ years \ later} = \dfrac{3}{5}$

$\sf \Longrightarrow \dfrac{5x + 5}{9x + 5} = \dfrac{3}{5}$

$\sf \Longrightarrow 5 \Big[ 5x + 5 \Big] = 3 \Big[9x + 5\Big]$

$\sf \Longrightarrow 25x + 25 = 27x + 15$

$\sf \Longrightarrow 25x - 27x = 15 - 25$

$\sf \Longrightarrow -2x = -10$

$\sf \Longrightarrow x = \dfrac{-10}{-2}$

$\sf \Longrightarrow x = 5$

Now, let's substitute the value of x in their present ages to find their present ages.

Albert's present age:

Albert's present age = 5x

Albert's present age = 5(5)

Albert's present age = 25 years old.

Salim's present age:

Salim's present age = 9x

Salim's present age = 9(5)

Salim's present age = 45 years old.

Therefore Albert is 25 years old and Salim is 45 years old.

Answer 2

${\underline{\purple{\frak{Question: - }}}}$

To find present ages of Albert and Salim

${\underline{\frak{\purple{Solution: - }}}}$

Given :

• The ratio of present ages of Albert and Salim is 5:9

• After 5 years, Ratio of their ages will be 3:5

Let,

• Present ages of Albert and Salim be 5x and 9x,

$\sf \: 5 : 9(after \: 5 \: years) \longrightarrow \: 3:5$

$\sf\rightarrow \small \frac{5x + 5}{9x + 5} = \frac{3}{5} \: (cross \: multiply) \\ \\ \sf\rightarrow \: 5(5x + 5) = 3(9x + 5) \\ \\ \sf\rightarrow \: 25x + 25 = 27x + 25 \\ \\ \sf\rightarrow \: 27 x - 25x = 25 - 15 \\ \\ \sf\rightarrow \: 2x = 10 \\ \\ \sf\rightarrow \: x = \frac{10}{2} \\ \\ {\boxed{\bf{x = 5}}}$

Then,

Present age Of Albert :

$\sf \: = 5x \\ =\sf 5 \times 5 \\ = \sf \: 25$

Present age of Salim :

$= \sf \: 9x \\ = \sf \: 9 \times 5 \\ = \sf \: 45$

So, Present ages of Albert and Salim is 25 and 45 .