Question

five years, hence the age of man will be three times that of his son. 5 years ago, the father age was 7 times the age of his son. what are their present age?

Answer 1

Solution :

Let the present age of man's be r years.

Let the present age of son's be m years.

A/q

$\underbrace{\bf{5\:years\:later\::}}}}$

The age of man will be (r+5) years.

The age of son will be (m+5) years.

$\longrightarrow\sf{(r+5)=3(m+5)}\\\\\longrightarrow\sf{r+5=3m+15}\\\\\longrightarrow\sf{r-3m=15-5}\\\\\longrightarrow\sf{r-3m=10}\\\\\longrightarrow\sf{r-3m=10.........................(1)}$

$\underbrace{\bf{5\:years\:ago\::}}}}$

The age of man will be (r-5) years.

The age of son will be (m-5) years.

$\longrightarrow\sf{(r-5)=7(m-5)}\\\\\longrightarrow\sf{r-5=7m-35}\\\\\longrightarrow\sf{r-7m=-35+5}\\\\\longrightarrow\sf{r-7m=-30}\\\\\longrightarrow\sf{r=-30+7m.........................(2)}$

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

$\longrightarrow\sf{-30+7m-3m=10}\\\\\longrightarrow\sf{-30+4m=10}\\\\\longrightarrow\sf{4m=10+30}\\\\\longrightarrow\sf{4m=40}\\\\\longrightarrow\sf{m=\cancel{40/4}}\\\\\longrightarrow\bf{m=10\:years}$

∴Putting the value of m in equation (2),we get;

$\longrightarrow\sf{r=-30+7(10)}\\\\\longrightarrow\sf{r=-30+70}\\\\\longrightarrow\bf{r=40\:years}$

Thus;

The present age of man's will be r = 40 years.

The present age of son's will be m = 10 years.

Answer 2

☆$\sf{\mathfrak{\underline{\pink{Given}}}}$

5 years ago, the father age was 7 times the age of his son.

five years, hence the age of man will be three times that of his son.

☆$\sf{\mathfrak{\underline{\purple{To\:Find}}}}$

find their present ages

☆$\sf{\mathfrak{\underline{\blue{Solution}}}}$

let the son's present age be y

let the father's present age be x

☆$\sf{\mathfrak{\underline{\underline{\green{\dag According \: to \: the\: question:-}}}}}$

➪ 5 years ago

the father age was 7 times the age of his son.

➦x - 5 = 7 ( y - 5 )

➦ x - 5 = 7y - 35

➦ x - 7y = -35 + 5

➦ x - 7y = - 30

➦ 7y - x = +30 --------( i )

➪ 5 years hence

the age of man will be three times that of his son.

➦ x + 5 = 3 ( y + 5 )

➦ x + 5 = 3y + 15

➦ x - 3y = 15 - 5

➦ x - 3y = 10 ----------( ii )

☆ Solving simultaneously

7y - x = 30

-3y + x = 10

_______________

4y = 40

y = 40 / 4

y = 10

_______________

• putting value of y in eq ( i )

➦7y - x = 30

➦7 x 10 - x = 30

➦70 - x = 30

➦ - x = 30 - 70

➦ - x = - 40

➦ x = 40

__________________________

☆Present age of the son $\sf{\mathfrak{\underline{\underline{\boxed{\orange{10\: years }}}}}}$

☆Present age of the father $\sf{\mathfrak{\underline{\underline{\boxed{\orange{40\: years }}}}}}$

___________________❤