Question

the present ages of A and B are in the ratio 2 : 3, after 6 yrs their ratio will become 3 : 4. what is the present age of A? ​

Answer 1

$\begin{gathered} \begin{gathered} \\ \underbrace{ \mathbb \red{ A } \green{n} \mathbb \blue{s} \purple{w} \mathbb \orange{e} \pink{r}:-} \: \end{gathered} \end{gathered}\mathbb \purple{ present \:age \:of \: A \:= 12\: years }$

$\red{ \sf \: let \: the \: present \: age \: of \: A \: be \: x }$

$\green{ \sf \: let \: the \: sum \: of \: ages \: of \: A = 2x \:and \: B = 3x}$

$\blue{ \sf \: after  \: 6  \: years \: , their \: ages \: are \: in \: ratio 3 : 4 }$

$\pink{ \sf \frac{2x + 6}{3x + 6} = \frac{3}{4} (cross\: multiplication)}$

$\purple{ \sf 8x + 24 = 9x + 18}$

$\red { \sf-1x = -6}$

$\green{ \sf \: x = \frac{-6}{-1} = 6 }$

$\blue{ \sf∴present \: age \: of \: A=2 \times 6 = 12\: years}$

$\pink{ \sf∴present \: age \: of \: B =3\times 6 = 18\: years}$

Answer 2

Given:-

present ages of A and B = 2:3

After 6 years, ages of A and B = 3:4

To find:-

The present age of A.

Answer:-

• Let the ratios of the present ages of A & B be 2x and 3x.
• 6 years hence, let their ages be in the ratios 3x & 4x.

∴Their ages will be 2x + 6 and 3x + 6.

And, the ratio of their ages are in the form 3/4.

Substitution:-

⇢ 2x + 6/3x + 6 = 3/4

⇢ 4(2x + 6) = 3(3x + 6) [∵performing cross multiplication.]

⇢ 8x + 24 = 9x + 18

⇢ 8x - 9x = 18 - 24

⇢ - 1x = - 6 [∵Minus on both sides get cancelled.]

∴x = 6

Hence their ages be,

➭Age of A = 2x = 2 (6) = 12 years.

➭Age of A = 3x = 3 (6) = 18 years.

∴The Age of A = 12 years.

Verification:-

➳ 12 + 6 = 18 years. (AGE OF A)

➳ 18 + 6 = 24 years. (AGE OF B)

So, the ratios are 18:24. (i.e), 3:4

As the ratios matches our answer is correct.