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

★${\underline{\underline{\large{\sf{Given:-}}}}}$

• 5 years ago, A was thrice as old as B.
• 10 years later, A shall be twice as old as B.

★${\underline{\underline{\large{\sf{To\:find:-}}}}}$

• Present age of A.

★${\underline{\underline{\large{\sf{Solution:-}}}}}$

Consider,

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

According to the 1st condition :-

• 5 years ago, A was thrice as old as B.

5 years ago,

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

$\to\sf{x-5=3(y-5)}$

$\to\sf{x-5=3y-15}$

$\to\sf{x=3y-10...........(i)}$

According to the 2nd condition :-

• 10 years later , A shall be twice as old as B .

10 years later,

• Age of A = (x+10) years
• Age of B = (y+10) years

$\to\sf{x+10=2(y+10)}$

$\to\sf{x+10=2y+20}$

• put x = 3y-10 from eq(1).

$\to\sf{3y-10+10=2y+20}$

$\to\sf{3y=2y+20}$

$\to\sf{3y-2y=20}$

$\to\sf{y=20}$

Now put y = 20 in eq(1) .

$\to\sf{x=3y-10}$

$\to\sf{x=3\times\:20-10}$

$\to\sf{x=50}$

• Present age of A = 50 years.

Answer 2

Present age of A is 50 years

Step-by-step explanation:

Let,

Five years ago,

Age of B = x

Age of A = 3x

Present age of B = x + 5

Present age of A = 3x + 5

10 years later,

A shall be twice as old as B

So,

The age of B = 2 (x + 5 + 10)

2x + 30

The age of A = 3x + 5 + 10

3x + 15

So,

⇒ 2x + 30 = 3x + 15

⇒ 2x - 3x = 15 - 30

⇒ - x = - 15

⇒ x = 15

★ Five years ago,

Age of B = 15 years

Age of A = 3x

⇒ 3 (15)

⇒ 3 × 15

⇒ 45

Age of A = 45 years

Age of B = 15 years

Present age of B = x + 5

⇒ 15 + 5

⇒ 20

Present age of A = 3x + 5

⇒ 45

⇒ 45 + 5

⇒ 50

Therefore,

Present age of A is 50 years