Question

Ten years ago, A was four times as old as B and after 10 years A will be twice as old as B find their present ages​

Answer 1

Solution :-

Let :-

Present age of A = x

Present age of B = y

Ten years ago :-

Age of A = x - 10

Age of B = y - 10

After ten years :-

Age of A = x + 10

Age of B = y + 10

According to the first condition :-

$\longrightarrow \sf x-10 = 4( y - 10 ) \\\\\longrightarrow x - 10 = 4y - 40 \\\\\longrightarrow x-4y = -30 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(1)$

According to the second condition :-

$\longrightarrow \sf x+10 = 2(y+10 ) \\\\\longrightarrow x+10 = 2y + 20 \\\\\longrightarrow x-2y = 10 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(2)$

Equation (2) - Equation (1) :-

$\longrightarrow \sf -2y = - 40 \\\\\longrightarrow \bf y = 20$

Substitute the value of y in eq (1) :-

$\longrightarrow \sf x - 4 \times 20 = - 30 \\\\\longrightarrow x- 80 = - 30 \\\\\longrightarrow \bf x = 50$

Present age of A = 50 years

Present age of B = 20 years

Answer 2

♡ Answer :

1. Present age of A = 50 years

1. Present age of B = 20 years

♡ Given:

• Ten years ago, A was four times as old as B

• After 10 years A will be twice as old as B

♡ To find:

• The ages of A and B

♡ Solution:

Let the Present age of "A" be "x" and present age of "B" be "y".

So, ten years ago :

$\hookrightarrow$ Age of A = x - 10

$\hookrightarrow$ Age of B = y - 10

According to this :

$\implies$ x - 10 = 4 ( y - 10 )

$\implies$ x - 10 = 4y - 40

$\implies$ x - 4y = (- 40) + 10

$\implies$ x - 4y = (-30) _____(i)

And After ten years :

$\hookrightarrow$ Age of A = x + 10

$\hookrightarrow$ Age of B = y + 10

According to this :

$\implies$x + 10 = 2 (y + 10)

$\implies$x + 10 = 2y + 20

$\implies$ x - 2y = 20 - 10

$\implies$x − 2y = 10 ______(ii)

By subtracting (ii) from (i) :-

$\implies$x - 2y - (x - 4y) = 10 - (-30)

$\implies$ x - 2y - x + 4y = 10 + 30

$\implies$ 4y − 2y = 40

$\implies$2y = 40

$\implies$ y = 20

By Substituting the value of y in (i), we get :

$\implies$x - (4 × 20) = (- 30)

$\implies$ x - 80 = (- 30)

$\implies$ x = (-30) + 80

$\implies$ x = 50

Therefore,

• Present age of A = 50 years

• Present age of B = 20 years

♡ Concepts Used:

• Assumption of unknown values

• Making expressions

• Equating the expressions

• Transposition Method

• Subtraction of equations

• Substitution of values