Question

the ages of A and B are in the ratio 8 : 3 . after 6 years hence their ages will be in the ratio 9:4 find their present ages ?​

Answer 1

Given :

• Ages of A and B are in the ratio $\rm \: 8:3$

• After $\rm\red {6 \: years}$, their ages will be in the ratio $\rm \: 9:4$

To Find :

• Their present ages.

Calculation :

Let,

• The present age of A be 8x
• The present age of B be 3x

$\underline{ \bf {After \: 6 \: years, }}$

• A's age will be 8x + 6
• B's age will be 3x + 6

$\dag$ According to the Question,

$\bullet \: \: \bf \dfrac{8x + 6}{3x + 6} \: = \dfrac{9}{4}$

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$\longrightarrow \rm \: 4 \: (3x + 6) = 9 \: (8x + 6) \\ \\ \\ \longrightarrow \rm \: 12x + 24 = 27 - 54 \\ \\ \\ \longrightarrow \rm \: 5x = 30 \\ \\ \\ \longrightarrow \rm \: x = \cancel \dfrac{30}{5} \\ \\ \\ \longrightarrow \boxed {\frak{ \red{x = 6}}} \star$

Henceforth,

A's age will be $\rm \: 8x$

$\longrightarrow \rm 8 \times 6 \\ \\ \\ \longrightarrow \boxed{\rm { \pink{48 \: years}}} \star$

B's age will be $\rm \: 3x$

$\longrightarrow \rm 3 \times 6 \\ \\ \\ \longrightarrow \boxed{\rm { \purple{18 \: years}}} \star$

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Therefore,

• A's present age = $\bf\pink {48 \: years }$
• B's present age = $\bf\purple {18 \: years}$

Answer 2

Answer:

$\rightarrow$ A= 48 years

$\rightarrow$ B = 18 years.

Step-by-step explanation:

We will first make understand the concept of the given question.

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$\rightarrow$ Ages of A and B at present = 8x, 3x

$\rightarrow$ Ages of A and B after 6years= 8x+6,3x+6

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Solution-

According to the question.

$\frac{8x + 6}{3x + 6} = \frac{9}{4} \\ \\ 32x + 24 = 27x + 54 \\ \\ 32x - 27x = 5 4 - 24 \\ \\ 5x = 30 \\ \\ x = \frac{30}{5} \\ \\ x = 6$

So,

Age of A = 6×8= 48 years

Age of B = 6×3 = 18 years.