Question

. The ages of A and B are in the ratio 2:3. Six years ago, their ages were in the ratio 3:5. Find their present ages​

Answer 1

Let the age of A be x years & B be y years

According to 1st condition

x/y=2/3

3x=2y

3x-2y=0 -(1)

Before 6 years,

Age of A =(x-6) years & B=(y-6) years

According to second condition,

x-6/y-6=3/5

5(x-6)=3(y-6)

5x-30=3y-18

5x-3y=-18+30

5x-3y=12 -(2)

Multiplying eqn (1) by 3 & (2) by 2

9x-6y=0 -(3)

10x-6y=24 -(4)

Subtracting eqn (3) from (4)

10x-6y=24

-9x+6y=0

x=24

Substituting x=24 in eqn (1)

3(24)-2y =0

72-2y=0

72=2y

y=36

PLEASE MARK IT AS BRAINLIEST

Answer 2

Answer:

A = 24 years

B = 36 years

Step-by-step explanation:

$\ggg \red{\underline{Question:-}}$

The ages of A and B are in the ratio 2:3. Six years ago, their ages were in the ratio 3:5. Find their present ages​?

$\ggg \red{\underline{Solution:-}}$

Let their present ages be = $2x$ $and$ $3x$

According to question,

$\Rightarrow \frac{2x-6}{3x-6} =\frac{3}{5}$

$\Rightarrow \frac{2x-6}{3x-6} \times\frac{3}{5} \:\: \:\: \:\:(cross \:\:multiplication)$

$\Rightarrow 5(2x-6) = 3(3x-6)$

$\Rightarrow 10x-30 = 9x-18$

$\Rightarrow x=-13+30 = 12$

$\boxed{x=12}$

Therefore,their present ages are

$A=2x=2(12)=24 \:years$

$B =3x=3(12)=36\:years$

$\boxed{\pink{A=24\:years\:\:B=36\:years}}$