Question

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

Answer 1

Answer:

A= 48 years and B=18 years

Answer 2

$\sf\pink{ Let \:us \:consider \:the\: ages \:as : }$

$\longrightarrow{\sf\pink{ 8x \:and\: 3x \:respectively}}$

We have been told that after six years the ratio will change .

$\sf\green{ So , \:we \:get\: the\: condition : }$

$\rm\green{ A = 8x + 6 }$

$\rm\green { B = 3x + 6}$

Then we will take the given condition ;

$\sf\purple{ \frac{8x + 6}{3x + 6} = \frac{9}{4}}$

When we cross multiply to remove the fractional form we get :

$\rm\red{ (8x + 6 \times 4) = ( 3x + 6 \times 9)}$

$\rm\red{ 32x + 24 = 27x + 54}$

After transposing the like terms we get :

$\rm\red{ 32x - 27x = 54 - 24}$

$\rm\red{ 5x = 30}$

$\rm\red{ x = \frac{30}{5}}$

$\rm\red{ x = 6 }$

We know that the present ages are :

$\sf\blue{ A = 8x }$

$\sf\blue{ B = 3x }$

We have found the value of x , now we will know the ages easily :

$\sf\orange{ 8x = 8\times 6 = 48 yrs.}$

$\sf\orange { 3x = 3 \times 6 = 18 yrs.}$