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

Step-by-step explanation:

Let the present age of Peter be x

And present age of Paul be y

Case 1:-

The sum of the ages of Peter and Paul is 24.

$\sf \implies x + y = 24.....(i)$

Case 2:-

Five years ago:-

Age of Peter = x - 5

Age of Paul = y - 5

Five years ago their ages were in the ratio 3:4.

$\sf \implies \dfrac{x - 5}{y - 5} = \dfrac{3}{4}$

$\sf \implies 4(x - 5) = 3(y - 5)$

$\sf \implies 4x - 20 = 3y - 15$

$\sf \implies 4x - 3y = -15 + 20$

$\sf \implies 4x - 3y = 5.....(ii)$

Multiply equation (i) with 4

$\sf \implies 4(x + y = 24)$

$\sf \implies 4x + 4y = 96.....(iii)$

Equation (iii) - (ii)

$\sf \implies 4x + 4y - (4x - 3y) = 96 - 5$

$\sf \implies 4x + 4y - 4x + 3y = 91$

$\sf \implies 7y = 91$

$\sf \implies y = 13$

Substitute y = 13 in equation (i)

$\sf \implies x + y = 24$

$\sf \implies x + 13 = 24$

$\sf \implies x = 24 - 13$

$\sf \implies x = 11$

Age of Peter after 3 years = x + 3 = 11 + 3 = 14

Age of Paul after 3 years = y + 3 = 13 + 3 = 16

After 3 years:-

Age of Peter = 14 years

Ahe of Paul = 16 years

Answer 2

Answer:

Given:-

• Sum of ages of peter and pual is 24
• Five years ago their ages ratio is 3:4

Find:-

• How old will they be in three years time?

Solution:-

Let take their present ages as x and y

Sum of their ages = 24

So, x + y = 24.....(1)

Let multiply with 4 in two sides

So, 4x + 4y = 96.....(2)

Five years ago their ages:-

Five years ago peter age = x - 5

Five years ago Paul age = y - 5

From question,

Ratio of their ages = 3:4

${ \implies{ \sf{ \: \: \frac{(x - 5)}{(y - 5)} = \frac{3}{4} }}}$

${ \implies{ \sf{ \: \: 4(x - 5) = 3(y - 5)}}}$

${ \implies{ \sf{ \: \: 4x - 20 = 3y - 15}}}$

${ \implies{ \sf{ \: \: 4x - 3y = - 15 + 20}}}$

${ \implies{ \sf{ \: \: 4x - 3y = 5......(3)}}}$

Solving equation (2) and (3) :-

${ \implies{ \sf{4x + 4y - 4x + 3y = 96 - 5}}}$

${ \implies{ \sf{ \: \: 4y + 3y = 91}}}$

${ \implies{ \sf{ \: \: 7y = 91}}}$

${ \implies{ \sf{ \: \: y = \frac{91}{7} = 13}}}$

So, value of y is 13

Let us substitute the value of y in equation (1)

${ \implies{ \sf{x + y = 24}}}$

${ \implies{ \sf{x + 13 = 24}}}$

${ \implies{ \sf{x = 24 - 13 = 11}}}$

So, value of x is 11

Present ages of Peter and Paul are 11 and 13

After three years:-

${ \therefore{ \sf{ \red{Age \: of \: Peter = 14}}}}$

${ \therefore{ \sf{ \red{Age \: of \: Paul = 16 }}}}$