Question

Two Years Ago Father Was Three Times As Old As His Son And Two Years Hence Twice His Age Will Be Equal To Five Times That Of His Son Find Their Presents Ages

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Answer 1

Answer:

Let us consider

Son's age = X

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Two years ago son's age X- 2

His Father's age at that time = 3(x - 2)

Present age of Father 3X - 6+ 2

The present age of Father = 3X - 4

Two years hence father's age = 3X - 4 + 2

Two years hence father's age 3X- 2

Two years hence son's age X + 2

Given:

5 x (X + 2) = 2 x (3x - 2)

5X + 10 = 6X -

X = 14

$hope \: it \: help \: you$

Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

Two years ago, father was three times as old as his son and two years hence, twice his age will be equal to 5 times that of his son.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

Their present ages.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the present age of father be r years.

Let the present age of his son be m years.

$\underbrace{\bf{Two\:years\:ago\::}}}}$

The father's age be (r-2) years.

The son's age be (m-2) years.

So;

$\longrightarrow\sf{(r-2)=3(m-2)}\\\\\longrightarrow\sf{r-2=3m-6}\\\\\longrightarrow\sf{r-3m=-6+2}\\\\\longrightarrow\sf{r-3m=-4}\\\\\longrightarrow\sf{r=-4+3m......................(1)}$

$\underbrace{\bf{After\:two\:years\::}}}}$

The father's age be (r+2) years.

The son's age be (m+2) years.

So;

$\longrightarrow\sf{2(r+2)=5(m+2)}\\\\\longrightarrow\sf{2r+4=5m+10}\\\\\longrightarrow\sf{2r-5m=10-4}\\\\\longrightarrow\sf{2r-5m=6}\\\\\longrightarrow\sf{2(-4+3m)-5m=6\:\:\:\:[from(1)]}\\\\\longrightarrow\sf{-8+6m-5m=6}\\\\\longrightarrow\sf{-8+m=6}\\\\\longrightarrow\sf{m=6+8}\\\\\longrightarrow\sf{\purple{m=14\:years}}$

Putting the value of m in equation (1),we get;

$\longrightarrow\sf{r=-4+3(14)}\\\\\longrightarrow\sf{r=-4+42}\\\\\longrightarrow\sf{\purple{r=38\:years}}$

Thus;

The present age of father is r = 38 years.

The present age of son is m = 14 years.