Question

Five years ago A was thrice as old as B and 10 years later A shall be twice as old as B, what is the present age of A?​

Answer 1

Given :-

• Five years ago A was thrice as old as B.

• Ten years later A shall be twice as old as B.

To Find :-

• What's the present age of A?

Solution :-

Let the present age of A be x years and the present age of B will be y years.

As per question :-

Given that,

Five years ago A was thrice as old as B.

Therefore,

five years ago ,

Age of A = ( x - 5) years

Age of B = ( y - 5) years

Again, it’s given that

Ten years later A shall be twice as old as B.

Ten years later,

Age of A = ( x +10) years

Age of B = ( y +10) years

According to the 1st condition :-

(x -5) = 3 ( y -5)

⟼ x -5 = 3y - 15

⟼ x - 3 y = -10.............. eq(1)

According to the second condition :-

(x + 10) = 2 ( y +10)

⟼ x +10 = 2y +20

⟼ x -2y = 10.......eq(2)

Find the value of x from eq(1)

x - 3 y = -10

⟼ x = -10 +3y

And put the value of x in eq(2)

x -2y = 10

⟼ -10 +3y -2y = 10

⟼ -10 +y = 10

⟼ y = 20

Therefore, present age of B is = 20 years

Now, put y = 20 in eq(1)

x - 3 y = -10

⟼ x - 3 × 20 = -10

$⟼x = 50$

Hence, present age of A is = 50 years

Answer 2

Given ,

• Five years ago , A was thrice as old as B

• Ten years later , A shall be twice as old as B

Let ,

• The present ages of A and B be x and y

According to the question ,

x - 5 = 3(y - 5)

x - 5 = 3y - 15

x - 3y = -10 --- (i)

And

x + 10 = 2(y + 10)

x + 10 = 2y + 20

x - 2y = 10 --- (ii)

Subtract eq (i) from eq (ii) , we get

x - 2y - (x - 3y) = 10 - (-10)

y = 20

Put y = 10 in eq (i) , we get

x - 3(20) = -10

x = 50

$\therefore$ The present age of A is 50