Question

Five years ago, Mr.x was three times as old as his son was then. Five years from now, Mr.z will be twice his son's age. Find their present ages

Answer 1

Given: Five years ago, Mr.x was three times as old as his son was then. Five years from now, Mr.x will be twice his son's age.

Need to find: Their present age?

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❍ So, Let's Consider the present age of Mr.x be x years and his son be y years respectively.

☆ Five years ago, their ages —

• Mr.x's age = (x – 5) years
• Son's age = (y – 5) years

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$\underline{\bigstar\:\boldsymbol{According\;to\;the\; Question\; :}}$⠀⠀

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• It is given that five years ago, the age of Mr.x was thrice the age of his son that is:

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

$:\implies\sf x - 5 = 3y - 15$

$:\implies\sf x - 3y = - 15 +5$

$:\implies\sf x - 3y = -10\;\;\qquad\qquad\bigg\lgroup\sf eq^n \;(1)\bigg\rgroup$

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☆ Five years from now, their ages —

• Mr.x's age = (x + 5) years
• Son's age = (y + 5) years

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⟩⟩ From the second given condition —

• Also, five years from now Mr.x will be twice as old as his son's age that is:

$:\implies\sf (x + 5) = 2(y +5)$

$:\implies\sf x + 5 = 2y +10$

$:\implies\sf x - 2y = 10 - 5$

$:\implies\sf x - 2y = 5\;\;\qquad\qquad\bigg\lgroup\sf eq^n \;(2)\bigg\rgroup$

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✇ Now, from eqₙ ( 1 ) & eqₙ ( 2 ) —

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$\dashrightarrow\sf x - x + (-2y + 3y) = 10 + 5$

$\dashrightarrow{\pmb{\sf{\purple{y = 15}}}}$

» Substituting the value of 'y' in eqₙ ( 2 ) —

$\dashrightarrow\sf x - 2y = 5$

$\dashrightarrow\sf x - 2(15) = 5$

$\dashrightarrow\sf x - 30 = 5$

$\dashrightarrow\sf x = 5 + 30$

$\dashrightarrow{\pmb{\sf{\purple{y = 35}}}}$

$\therefore{\underline{\textsf{Hence, the present age of Mr.x and his son is \textbf{35 years} \sf{\&} \textbf{15 years}.}}}$

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Answer 2

Answer:

Father age = 35

Son age = 15

Solution:

Let father's age be X and son's age be Y

Now according to Question

5Years back

→ X-5=3(Y-5)

→ X-3Y=-10 ------------------------------(1)

5 Years from now

→ X+5=2(Y+5)

→ X-2Y=5--------------------------------(2)

Subtract EQ 1 from 2

→ X-2Y-(X-3Y)=5-(-10)

→ Y=15

put the valye of Y in any equation to find X

hence

→ X-45=-10

→ X=35

Answer X= 35 and Y= 15