Question

The present ages of Prateek and
Gopal are in the ratio of 5:7. Three
years ago, Gopal was six years older
to Prateek. What will be the ratio of
their ages six years hence ? So​

Answer 1

Prateek's age after 6 years=33 years

Gopal's age after 6 years=39 years

Explanation:

Let

• Prateek's age be x
• Gopal's age be y.

Their present ages are,

• Prateek's age=5x
• Gopal's age=7y.

Given,

• Gopal's present age=Prateek's present age
• 7y=5x
• 7y-5x=0(5x is transposed to the other side)

Let 7y-5x=0 be Equation 1.

3 years ago,

• Prateek's age=5x-3
• Gopal's age=7y-3+6

Also given,

• Gopal's age 3 years ago=Prateek's age 3 years ago
• 7y-3+6=5x-3
• 7y+3=5x-3
• 7y-5x+3=-3(5x is transposed to the other side)
• -5x+7y=-3-3(+3 is transposed to the other side)
• -5x+7y=-6

Let -5x+7y=-6 as Equation 2.

{Equation 1} 7y-5x= 0

{Equation 2}-5x+7y=-6(Using elimination by substitution method)

{Equation 2} -5x+7y=-6

• 7y=-6+5x(-5x is transposed to the other side)
• y=(-6+5x)/7

Let y=(-6+5x)/7 be Equation 3.

{Equation 1}7y-5x=0

• 7[(-6+5x)/7]+5x=0[y=(-6+5x)/7]
• -6+5x+5x=0
• -6+10x=0
• 10x=6(6 is transposed to other side)
• x=6/10(10 is transposed to the other side)
• x=3/5(6/10 is simplified)

{Equation 3}y=(-6+5x)/7

• y=[-6+5(3/5)]/7(x=3/5)
• y=[-6+3]/7
• y=[-3]/7
• y=-3/7

6 years hence,

• Prateek's age=x+6 years

=3/5+6(x=3/5)

=3/5+6/1

LCM=5

Multiply by 5

=5(3)/5+5(6)/1

=3+30

=33

Prateek's age after 6 years=33 years

• Gopal's age=y+6 years

=-3/7+6(y=-3/7)

=-3/7+6/1

LCM=7

Multiply by 7

=7(-3)/7+7(6)/1

=-3+42

=39

Gopal's age after 6 years=39 years

Is my answer correct and I have not copy pasted it but did it on my own on the spot!?