Question

two years ago,a father was five times as old as his son.two years later,his age will be 8 more than three times the age of the son . find the present ages of father and son .​

Answer 1

Step-by-step explanation:

2 years ago,son was x years old

father was 5x years old

at present son is x+2,father is 5x+2

2years later,son is x+4,father is 5x+4

5x+4=3(x+4)+8

5x-3x=12+8-4=16

2x=16

x=16/2=8

present age of the son is8+2years=10 years

present age of the father is 5.8+2=42 years

Answer 2

GivEn:

• Two years ago, a father was five times as old as his son.

• Two years later, his age will be 8 more than three times the age of the son.

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To find:

• Present age of father and his son.

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SoluTion:

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☯ Let present age of father be x years.

☯ Let present age of his son be y years.

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${\underline{\bf{\bigstar\;As\;per\:given\;question\;:}}}$

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Two years ago,

Father was five times as old as his son.

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Therefore,

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Ages before two year,

• Age of father = (x - 2) years
• Age of his son = (y - 2) years

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

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

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

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$:\implies\bf x = 5y - 8\;\;\;\;\;\;\;\;\:\bigg\lgroup\bf eq.\;(1)\bigg\rgroup$

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Two year later,

Age of father will be 8 more than three times the age of the son.

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Therefore,

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Ages after two year,

• Age of father = (x + 2) years
• Age of his son = (y + 2) years

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$:\implies\sf x + 2 = 3(y + 2) + 8$

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$:\implies\sf x + 2 = 3y + 6 + 8$

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$:\implies\sf x + 2 = 3y + 14$

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$:\implies\sf x = 3y + 14 - 2$

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$:\implies\bf x = 3y + 12\;\;\;\;\;\;\;\;\:\bigg\lgroup\bf eq.\;(2)\bigg\rgroup$

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${\underline{\sf{\bigstar\;Now,\; According\;to\:eq.(1)\;and\;eq.(2)\;:}}}$

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$:\implies\sf 5y - 8 = 3y + 12$

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$:\implies\sf 5y - 3y = 12 + 8$

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$:\implies\sf 2y = 20$

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$:\implies\sf y = \cancel{ \dfrac{20}{2}}$

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$:\implies{\underline{\boxed{\bf{\pink{y = 10\;years}}}}}\;\bigstar$

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${\underline{\sf{\bigstar\;Put\;value\;of\;y\;in\;eq\;(1)\;:}}}$

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$:\implies\sf x = 5 \times 10 - 8$

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$:\implies\sf x = 50 - 8$

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$:\implies{\underline{\boxed{\bf{\purple{x = 42\;years}}}}}\;\bigstar$

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$\therefore$ Present age of father is 42 years and Present age of his son is 20 years.