Question

Joseph age is three times that of ramus age. Before 5years Joseph age was four times that of ramu. Then what is the present age of ramu and Joseph!?

Answer 1

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

$\sf{\implies The\: present\:age\:of\: Joseph=x}$

$\sf{\implies The\: present\:age\:of\:Ramu=y}$

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

$\bf{\implies The\: present\:age\:of\:_{(Joseph\:and\:Ramu)}=?}$

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

• According to question we have to set up eq then solve the equation to find the the present age of Joseph and Ramu.]

$\sf\small\underline{Given\:in\:case\:(i):}$

• Joseph age is 3 times the age of Ramu]

$\tt{\implies Joseph\:_{(age)}=3\times\:Ramu\:_{(age)}}$

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

$\sf\small\underline{Given\:in\:case\:(ii):}$

• Before 5 years Joseph's age was 4 times the age of Ramu.]

$\tt{\implies Joseph\:_{(age\:5\: years\:ago)}=4\times\:Ramu\:_{(age\:5\: years\:ago)}}$

$\tt{\implies x-5=4(y-5)}$

$\tt{\implies x-5=4y-20}$

$\tt{\implies x-4y=-20+5}$

$\tt{\implies x-4y=-15-------(ii)}$

• In eq (ii) putting the value of x=3y here]

$\tt{\implies x-4y=-15}$

$\tt{\implies 3y-4y=-15}$

$\tt{\implies -y=-15\implies y=15}$

• Now, putting the value of y=15 in eq (i)]

$\tt{\implies x=3y\implies x=3(15)=45}$

$\sf\large{Hence,}$

$\sf{\implies The\: present\:age\:of\: Joseph=45\: years}$

$\sf{\implies The\: present\:age\:of\:Ramu=15\: years}$

Answer 2

Let

the age of Joseph=x

the age of Ramu=x

Find: Their present age=?

solutions

x=3y-----1

again in equation

x-5=4(y-5)

x-4y=-15

substitute the value of x=3y here

3y-4y=-15

y=15

now put value of y

x=3y

x=3×15=45

therefore, Joseph age=45 year s

Ramu age=15 years