Question

The sum of the ages of Peter and Paul is 24. Five years ago their respective ages were in the ratio 3:4. How old
will they be in three years’ time?

Answer 1

Let, their present ages be x and y respectively.

So, (x+y) = 24

Or, 4x +4y =96 - - - - (1)

And, (x-5)/(y-5)=3/4

Or, 4x-20=3y-15

Or, 4x - 3y =5——-(2)

Solving equations (1) and (2), we get - - -

4x +4y - 4x +3y =96-5=91

Or, 7y =91

Or, y =91/7=13

So, x =24–13=11

So,their present ages are 11 and 13 respectively.

After, 3 years, their ages will be 14 and 16 years

Hence, the ratio will be = 14:16=7:8 (answer)

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Answer 2

Given :

• Sum of the ages of Peter and Paul is 24.
• Ratio of their ages before 5 years is 3:4.

To find :

• Age of Peter and Paul after 3 years?

Solution :

⌬ Let present age Peter be x years.

⌬ And, Present age of Paul be y years.

Given that,

• Sum of the ages of Peter and Paul is 24.

⇒ x + y = 24 eq

⇒ x = 24 - y ⠀⠀⠀⠀⠀⠀⠀❬ eq (1) ❭

⠀━━━━━━━━━━━━━━━━━━━━

★ According to the Question:

• Ratio of their ages before 5 years is 3:4.

Their ages before 5 years,

• Age of Peter = (x - 5) years
• Age of Paul = (y - 5) years

Therefore,

⇒ (x - 5)/(y - 5) = 3/4

⇒ 4(x - 5) = 3(y - 5)

⇒ 4x - 20 = 3y - 15 eq

⇒ 4x - 3y = - 15 + 20

⇒ 4x - 3y = 5⠀⠀⠀⠀⠀⠀⠀ ❬ eq (2) ❭

⠀━━━━━━━━━━━━━━━━━━━━

Substituting eq (1) in eq (2),

⇒ 4(24 - y) - 3y = 5

⇒ 96 - 4y - 3y = 5

⇒ 96 - 7y = 5

⇒ - 7y = 5 - 96

⇒ - 7y = - 91

⇒ y = 91/7

⇒ y = 13

⠀━━━━━━━━━━━━━━━━━━━━

Now, Putting value of y in eq (1),

⇒ x = 24 - 13

⇒ x = 11

Therefore,

• Age of Peter after 3 years = x + 3 = 11 + 3 = 14 years
• Age of Paul after 3 years = y + 3 = 13 + 3 = 16 years

∴ Hence, Age of Peter and Paul after 3 years is 14 years and 16 years respectively.