Question

The difference between age of two brothers is 3 years five years ago the younger was 2/5 times the age of elder brother and their present age

Answer 1

$\sf\large\underline{Let:}$

$\rm{The\: present\: age\:of\:elder\: brother=x\: year's}$

$\rm{The\: present\:age\:of\: younger\: brother=y\:year's}$

$\sf\large\underline{To\: Find:}$

$\rm{The\: present\:age\:two\: brother's}$

$\sf\large\underline{Solution:}$

$\sf\large\underline{Given:in\:1st\:case:}$

$\rm{The\: difference\: between\:age\:two\: brothers=3}$

$\rm{\implies x-y=3}$

$\rm\green{\implies x-y=3------(i)}$

$\rm{\implies x=3+y}$

$\sf\large\underline{Given:in\:2nd\:case:}$

$\rm{Five\: years\:ago\: younger\:was\:2/5\: times\:the\:age\:of\: elder\: brother}$

$\rm{\implies y-5=\dfrac{2}{5}(x-5)}$

$\rm{\implies 2x-10=5y-25}$

$\rm{\implies 2x-5y=-25+10}$

$\rm\red{\implies 2x-5y=-15------(ii)}$

• [Putting the value of X=3+y in eq ii]

$\rm{\implies 2x-5y=-15}$

$\rm{\implies 2(3+y)-5y=-15}$

$\rm{\implies 6+2y-5y=-15}$

$\rm{\implies -3y=-15-6}$

$\rm{\implies -3y=-21}$

$\rm\red{\implies y=7}$

• [putting the value of y=7 in i]

$\rm{\implies x-y=3}$

$\rm{\implies x-7=3}$

$\rm{\implies x=3+7}$

$\rm\red{\implies x=10}$

Hence,

$\rm{\implies The\: present\:age\:of\: elder\: brother=10\: year's}$

$\rm{\implies The\: present\:age\:of\: younger\: brother=7\: year's}$

Answer 2

Given :

• Difference between age of two brothers = 3 years
• 5 years ago, the younger was 2/5 times the age of elder brother.

To find :

• Their present ages.

Solution :

Consider,

• Age of elder brother = x years
• Age of younger brother = y years

According to the 1st condition :-

• Difference between age of two brothers is 3 years

$\implies\sf{x-y=3}$

$\implies\sf{x=3+y............(1)}$

According to the 2nd condition :-

• 5 years ago, the younger was 2/5 times the age of elder brother.

5 years ago,

• Age of elder brother = (x-5) years
• Age of younger brother = (y-5) years

$\implies\sf{\dfrac{2}{5}\times\:(x-5)=(y-5)}$

$\implies\sf{2x-10=5y-25}$

$\implies\sf{2(3+y)-10=5y-25\:[put\:x=(3+y)\: from\:eq(1)]}$

$\implies\sf{6+2y-10=5y-25}$

$\implies\sf{2y-5y=-25-6+10}$

$\implies\sf{-3y=-21}$

$\implies\sf{y=7}$

Now put y = 7 in eq (1) for getting the value of x .

$\implies\sf{x=3+y}$

$\implies\sf{x=3+7}$

$\implies\sf{x=10}$

Therefore, the present age of elder brother is 10 years and the present age of younger brother is 7 years.