Question

The sum of the ages of two persons A and B is 50. five years ago, the ratio of their ages was 5:3. the present age of A and B are​

Answer 1

$\textbf{Answer :}$

→ Suppose the age of person A is x years

→ Since the sum of ages of both persons = 50,

$\textbf{Age of person B = 50-x}$

$\textbf{ \red{5 years ago :}}$

→ Age of person A = x-5

→ Age of person B = 50-x-5 = 45-x

→ Since 5 years ago,

$\textbf{Ratio of their ages was 5:3,}$

$\tt{=> \frac{(45-x)}{(x-5)} = \frac{5}{3}}$

$\tt{=> 3 \: (45-x) = 5 \: (x-5)}$

$\tt{=> 135 - 3x = 5x - 25}$

$\tt{=> 8x = 160}$

$\tt{=> {x = 20}}$

$\tt{=>{50 \: - \: x = 30}}$

$\tt{Present \: age \: of \: person \: A \: is \: 20 \: years}$

$\tt{Present \: age \: of \: person \: B \: is \: 30 \: years}$

Answer 2

Answer:

Person A is 30 years old and person B is 20 years old.

Step-by-step explanation:

a + b = 50

$\frac{a-5}{b-5}$ = $\frac{5}{3}$ ⇔ 3a - 15 = 5b - 25 ⇔ 3a - 5b = - 10

$\left \{ {{a+b=50} \atop {3a-5b=-10}} \right.$

(1) × 5 + (2)

8a = 240 ⇒ a = 30, then b = 20

Person A is 30 years old and person B is 20 years old.