Question

5 years ago Ahsan's age was 7 times of Shakeel's age but after 3 years Ahsan's age will be 4 times of Shakeel's age.Calculate their ages
(The equation should be constructed and solved with one variation)​

Answer 1

Step-by-step explanation:

Let the present age of Ahsan is x

And The present age of Shakeel be y

Case 1:-

5 years ago:-

Age of Ahsan = x - 5

Age of Shakeel = y - 5

Given, Ahsan's age was 7 times as that of Shakeel

$\sf \longrightarrow x - 5 = 7(y - 5)$

$\sf \longrightarrow x - 5 = 7y - 35$

$\sf \longrightarrow x - 7y = -35 + 5$

$\sf \longrightarrow x - 7y = -30......(i)$

Case 2:-

After 3 years:-

Age of Ahsan = x + 3

Age of Shakeel = y + 3

Given, Ahsan will be 4 times as old as him.

$\sf \longrightarrow x + 3 = 4(y + 3)$

$\sf \longrightarrow x + 3 = 4y + 12$

$\sf \longrightarrow x - 4y = 12 - 3$

$\sf \longrightarrow x - 4y = 9.....(ii)$

Equation (ii) - (i)

$\sf \longrightarrow x - 4y - (x - 7y) = 9 -(-30)$

$\sf \longrightarrow x - 4y - x + 7y= 9 + 30$

$\sf \longrightarrow 3y = 39$

$\sf \longrightarrow y = \dfrac{39}{3} = 13$

Substitute y = 13 in (ii)

$\sf \longrightarrow x - 4y = 9$

$\sf \longrightarrow x - 4(13) = 9$

$\sf \longrightarrow x = 9 + 52$

$\sf \longrightarrow x = 61$

Therefore:-

Present age of Ahsan = 61 years

Present age of Shakeel = 13 years

Answer 2

$\bf \huge \pink ◆ Explanation -$

• Let the present age of Ahsan is x

• And The present age of Shakeel be y

Case 1:-

5 years ago:-

Age of Ahsan = x - 5

Age of Shakeel = y - 5

Given, Ahsan's age was 7 times as that of Shakeel

• $x−5=7(y−5)$

• $x−5=7y−35$

• $x−7y=−35+5$

• $x−7y=−30......(i)$

Case 2:-

After 3 years:-

Age of Ahsan = x + 3

Age of Shakeel = y + 3

Given, Ahsan will be 4 times as old as him.

• $x+3=4(y+3)$

• $x+3=4y+12$

• $x−4y=12−3$

• $x−4y=9.....(ii)$

Equation (ii) - (i)

• $x−4y−(x−7y)=9−(−30)$

• $x−4y−x+7y=9+30$

• $3y=39$

• $y= \dfrac{39}{3} =13$

Substitute y = 13 in (ii)

• $x−4y=9$

• $x−4(13)=9$

• $x=9+52$

• $x=61$

Therefore:-

Present age of Ahsan = 61 years

Present age of Shakeel = 13 years