Question

The age of B is five years more than that of A. Five years ago, the ratioof A's age to B's age was 4:5. What are their present ages?​

Answer 1

Given :

• The age of B is 5 years more than the age of A.
• 5 years ago, the ratio of A's age to the B's age was 4:5.

To find :

• Their present ages.

Solution :

Consider,

• Present age of A = x
• Present age of B = y

According to the 1st condition :-

• The age of B is 5 years more than the age of A.

$\to\sf{y=x+5...............(1)}$

According to the 2nd condition :-

• 5 years ago, the ratio of A's age to the B's age was 4:5.

5 years ago,

• Age of A = (x-5) years
• Age of B = (y-5) years

$\to\sf{(x-5):(y-5)=4:5}$

$\to\sf{\dfrac{x-5}{y-5}=\dfrac{4}{5}}$

$\to\sf{\dfrac{x-5}{x+5-5}=\dfrac{4}{5}\:[put\:y=x+5\: from\:eq(1)]}$

$\to\sf{\dfrac{x-5}{x}=\dfrac{4}{5}}$

$\to\sf{5x-25=4x}$

$\to\sf{5x-4x=25}$

$\to\sf{x=25}$

• Present age of A = 25 years

Now put x = 25 in eq(1) for getting the value of y.

$\to\sf{y=x+5}$

$\to\sf{y=25+5}$

$\to\sf{y=30}$

• Present age of B = 30 years

Therefore, the present age of A is 25 years and the present age of B is 30 years.

Answer 2

S O L U T I O N :

Let the present age of A's be R years.

Let the present age of B's be (R+5) years.

$\underbrace{\sf{5\:years\:agO\::}}}}$

The age of A's = (R-5) years.

The age of B's = (R+5-5) years.

A/q

$\longrightarrow\rm{\dfrac{R-5}{R} =\dfrac{4}{5}} \\\\\longrightarrow\rm{5(R-5)=4R}\\\\\longrightarrow\rm{5R-25=4R}\\\\\longrightarrow\rm{5R-4R=25}\\\\\longrightarrow\bf{R=25\:years}$

Thus;

$\underbrace{\sf{The\:present\:age\:of\:A's\:will\:be\:r=\boxed{\bf{25\:years.}}}}}\\\\\underbrace{\sf{The\:present\:age\:of\:B's\:will\:be\:(r+5)=(25+5)=\boxed{\bf{30\:years.}}}}}$