Question

the age of a and b are in ratio 5:7 5years from now their ratio of their age will be 3:4 find their present age​

Answer 1

Solution :

$\bf{\small{\red{\underline{\bf{Given\::}}}}}$

The age of a and b are in the ratio 5:7, 5 years from now their ratio of their ages will be 3:4.

$\bf{\small{\red{\underline{\bf{To\:find\::}}}}}$

The present ages.

$\bf{\small{\red{\underline{\bf{Explanation\::}}}}}$

Let the present age of a be 5r years.

Let the present age of b be 7r years.

So;

$\underline{\underline{\bf{After\:5\:years\::}}}}$

The age of a be (5r + 5) years

The age of b be (7r + 5) years

A/q

$\longrightarrow\sf{\dfrac{5r+5}{7r+5} =\dfrac{3}{4} }\\\\\\\longrightarrow\sf{4(5r+5)=3(7r+5)}\\\\\\\longrightarrow\sf{20r+20=21r+15}\\\\\\\longrightarrow\sf{20r-21r=15-20}\\\\\\\longrightarrow\sf{\cancel{-}r=\cancel{-}5}\\\\\\\longrightarrow\sf{\red{r=5\:years}}$

Thus;

The present age of a = 5r = 5(5) = 25 years.

The present age of b = 7r = 7(5) = 35 years.

Answer 2

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QUESTION -

The age of a and b are in ratio 5:7 .

5 years from now their ratio of their age will be 3:4 .

Fiind their present ages.

SOLUTION :

From the above Question, we can gather the following information...

The age of a and b are in ratio 5:7 .

5 years from now their ratio of their age will be 3:4 ..

Let their ages be 5 x and 7 x respectively.

Now,

After 5 years,

Age Of A = 5x + 5

Age of B = 7x + 5

This ratio is 3 : 4.

So,

$\therefore { \dfrac{5x+5}{7x+5} = \dfrac{3}{4} }$

$=> 21x + 15 = 20x + 20 \\ \\ => x = 5$

Age Of A = 5x = 25 years.

Age Of B = 7x = 35 years.