Question

The age of A and B is 3:8 . After 6 years the age will 4:9. So what is the present age of A ?

Answer 1

Question:

The ratio of present ages of A and B is 3:8 . After 6 years , their ages will be in ratio 4:9. Find the present age of A.

Answer:

Present age of A is 18 years.

Solution:

It is given that;

The ratio of present ages of A and B is 3:8 .

Thus,

Let the present age of A be 3x years

and the present age of B be 8x years .

Hence,

Age of A after 6 years = (3x+6) years

And ,

Age of B after 6 years = (8x+6) years.

Now,

According to the question;

After 6 years , ages of A and B will be in ratio 4:9.

Thus;

=> (3x+6):(8x+6) = 4:9

=> (3x+6)/(8x+6) = 4/9

=> 9•(3x+6) = 4•(8x+6)

=> 27x + 54 = 32x + 24

=> 32x - 27x = 54 - 24

=> 5x = 30

=> x = 30/5

=> x = 6

Hence,

Present age of A

= 3x years

= 3•6 years

= 18 years

Also,

Present age of B

= 8x years

= 8•6 years

= 48 years

Answer 2

SOLUTION:-

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Given:

The age of A & B is 3:8. After 6 years the age will 4:9.

To find:

══════

The present age of A.

Explanation:

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Assume the age be R years.

Let the age of A:B= 3R:8R

After 6 years:

The age will be 4:9

$\frac{3r + 6}{8r + 6}$

According to the question:

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$= > \frac{3R + 6}{8R + 6} = \frac{4}{9} \\ \\ [cross \: multiplication] \\ \\ = > 27R + 54 = 32R + 24 \\ \\ = > 27R - 32R = 24 - 54 \\ \\ = > - 5R = - 30 \\ \\ = > 5R= 30 \\ \\ = > R = \frac{30}{5} \\ \\ = > R = 6 \: years$

Now,

The present age of A is 3R.

=) 3×6

=) 18 years.

:)