Question

Q- Five years ago, Pradeep was thrice as old as Vinay. Ten years later, Pradeep will be twice as old as Vinay. How old are Pradeep and Vinay?

(wrote the question too in case you didn't get my writing or photo is unclear which obviously makes the purpose of attaching the photo useless)​

Answer 1

Answer:

Answer:

Age of the Pradeep is = 50 years

Age of the Vinay is = 20 years

$\checkmark$Given:

$\textsf{Five years ago Pradeep was thrice as old as Vinay}$

$\textsf{Ten years later,Pradeep will be twice as old as Vinay}$

$\checkmark$To find:

(i) Age of the Pradeep

(ii) Age of the Vinay

$\checkmark$Taken:

Let the age of the Pradeep be x

And let the age of the Vinaj be y

The first equation which will be form is:.........................(i)

$(x-5)=3(y-5)$

(-5 because it is given 5 years ago)

The second equation which will be form is:................(ii)

$(x+10)=2(y+10)$

(+10 because it is given 10 years later)

$\checkmark$Concept:

First find the value of both the equation. Take both the equation by substituting the x to find the age of y .

$\checkmark$Solution:

Equation (i) :

$Taken,(x-5)=3(y-5)$

$\mapsto{(x-5)=3(y-5)}$

$\mapsto{x-5=3y-15}$

$\mapsto{-5+15=3y-x}$

$\mapsto{10=3y-x}$..............(i)

___________________________________

Equation (ii) :

$Taken,(x+10)=2(y+10)$

$\mapsto{(x+10)=2(y+10)}$

$\mapsto{x+10=2y+20}$

$\mapsto{x=2y+20-10}$

$\mapsto{x=2y+10}$..............(ii)

___________________________________

Substituting the value of x and find the age of y :

$\mapsto{3y-2y-10=10}$

$\mapsto{y=10+10}$

$\mapsto{y=20\:years}$

____________________________________

Now , find the age of x :

Taking the equation (ii)

$\mapsto{x=2y+10}$

$\mapsto{x=(2×20)+10}$

$\mapsto{x=40+10}$

$\mapsto{x=50\:years}$

So , the age of Pradeep and Vinay is 20 years and 50 years respectively.

▪︎ Additional information ▪︎

First equation of motion :

$Vf = Vi + at$

Where,

Vf = Final velocity

Vi = Initial velocity

a = Acceleration

t = Time taken

Second equation of motion:

$s=ut+\frac{1}{2}at²$

Where,

s = Distance travelled

u = Initial velocity

a = Acceleration

t = Time taken

Third equation of motion:

$v²=u²+2aS$

Where,

v = Final velocity

u = Initial velocity

a = Acceleration

S = Displacement

Answer 2

$Answer:</p><p></p><p>Age of the Pradeep is = 50 years</p><p></p><p>Age of the Vinay is = 20 years</p><p></p><p>\checkmark✓ Given:</p><p></p><p>\textsf{Five years ago Pradeep was thrice as old as Vinay}Five years ago Pradeep was thrice as old as Vinay</p><p></p><p>\textsf{Ten years later,Pradeep will be twice as old as Vinay}Ten years later,Pradeep will be twice as old as Vinay</p><p></p><p>\checkmark✓ To find:</p><p></p><p>(i) Age of the Pradeep</p><p></p><p>(ii) Age of the Vinay</p><p></p><p>\checkmark✓ Taken:</p><p></p><p>Let the age of the Pradeep be x</p><p></p><p>And let the age of the Vinaj be y</p><p></p><p>The first equation which will be form is:.........................(i)</p><p></p><p>(x-5)=3(y-5)(x−5)=3(y−5)</p><p></p><p>(-5 because it is given 5 years ago)</p><p></p><p>The second equation which will be form is:................(ii)</p><p></p><p>(x+10)=2(y+10)(x+10)=2(y+10)</p><p></p><p>(+10 because it is given 10 years later)</p><p></p><p>\checkmark✓ Concept:</p><p></p><p>First find the value of both the equation. Take both the equation by substituting the x to find the age of y .</p><p></p><p>\checkmark✓ Solution:</p><p></p><p>Equation (i) :</p><p></p><p>Taken,(x-5)=3(y-5)Taken,(x−5)=3(y−5)</p><p></p><p>\mapsto{(x-5)=3(y-5)}↦(x−5)=3(y−5)</p><p></p><p>\mapsto{x-5=3y-15}↦x−5=3y−15</p><p></p><p>\mapsto{-5+15=3y-x}↦−5+15=3y−x</p><p></p><p>\mapsto{10=3y-x}↦10=3y−x ..............(i)</p><p></p><p>___________________________________</p><p></p><p>Equation (ii) :</p><p></p><p>Taken,(x+10)=2(y+10)Taken,(x+10)=2(y+10)</p><p></p><p>\mapsto{(x+10)=2(y+10)}↦(x+10)=2(y+10)</p><p></p><p>\mapsto{x+10=2y+20}↦x+10=2y+20</p><p></p><p>\mapsto{x=2y+20-10}↦x=2y+20−10</p><p></p><p>\mapsto{x=2y+10}↦x=2y+10 ..............(ii)</p><p></p><p>___________________________________</p><p></p><p>Substituting the value of x and find the age of y :</p><p></p><p>\mapsto{3y-2y-10=10}↦3y−2y−10=10</p><p></p><p>\mapsto{y=10+10}↦y=10+10</p><p></p><p>\mapsto{y=20\:years}↦y=20years</p><p></p><p>____________________________________</p><p></p><p>Now , find the age of x :</p><p></p><p>Taking the equation (ii)</p><p></p><p>\mapsto{x=2y+10}↦x=2y+10</p><p></p><p>\mapsto{x=(2×20)+10}↦x=(2×20)+10</p><p></p><p>\mapsto{x=40+10}↦x=40+10</p><p></p><p>\mapsto{x=50\:years}↦x=50years</p><p></p><p>So , the age of Pradeep and Vinay is 20 years and 50 years respectively.</p><p></p><p>▪︎ Additional information ▪︎</p><p></p><p>First equation of motion :</p><p></p><p>Vf = Vi + atVf=Vi+at</p><p></p><p>Where,</p><p></p><p>Vf = Final velocity</p><p></p><p>Vi = Initial velocity</p><p></p><p>a = Acceleration</p><p></p><p>t = Time taken</p><p></p><p>Second equation of motion:</p><p></p><p>s=ut+\frac{1}{2}at²s=ut+21at²</p><p></p><p>Where,</p><p></p><p>s = Distance travelled</p><p></p><p>u = Initial velocity</p><p></p><p>a = Acceleration</p><p></p><p>t = Time taken</p><p></p><p>Third equation of motion:</p><p></p><p>v²=u²+2aSv²=u²+2aS</p><p></p><p>Where,</p><p></p><p>v = Final velocity</p><p></p><p>u = Initial velocity</p><p></p><p>a = Acceleration</p><p></p><p>S = Displacement</p><p></p><p>Answer:</p><p></p><p>Age of the Pradeep is = 50 years</p><p></p><p>Age of the Vinay is = 20 years</p><p></p><p>\checkmark✓ Given:</p><p></p><p>\textsf{Five years ago Pradeep was thrice as old as Vinay}Five years ago Pradeep was thrice as old as Vinay</p><p></p><p>\textsf{Ten years later,Pradeep will be twice as old as Vinay}Ten years later,Pradeep will be twice as old as Vinay</p><p></p><p>\checkmark✓ To find:</p><p></p><p>(i) Age of the Pradeep</p><p></p><p>(ii) Age of the Vinay</p><p></p><p>\checkmark✓ Taken:</p><p></p><p>Let the age of the Pradeep be x</p><p></p><p>And let the age of the Vinaj be y</p><p></p><p>The first equation which will be form is:.........................(i)</p><p></p><p>(x-5)=3(y-5)(x−5)=3(y−5)</p><p></p><p>(-5 because it is given 5 years ago)</p><p></p><p>The second equation which will be form is:................(ii)</p><p></p><p>(x+10)=2(y+10)(x+10)=2(y+10)</p><p></p><p>(+10 because it is given 10 years later)</p><p></p><p>\checkmark✓ Concept:</p><p></p><p>First find the value of both the equation. Take both the equation by substituting the x to find the age of y .</p><p></p><p>\checkmark✓ Solution:</p><p></p><p>Equation (i) :</p><p></p><p>Taken,(x-5)=3(y-5)Taken,(x−5)=3(y−5)</p><p></p><p>\mapsto{(x-5)=3(y-5)}↦(x−5)=3(y−5)</p><p></p><p>\mapsto{x-5=3y-15}↦x−5=3y−15</p><p></p><p>\mapsto{-5+15=3y-x}↦−5+15=3y−x</p><p></p><p>\mapsto{10=3y-x}↦10=3y−x ..............(i)</p><p></p><p>___________________________________</p><p></p><p>Equation (ii) :</p><p></p><p>Taken,(x+10)=2(y+10)Taken,(x+10)=2(y+10)</p><p></p><p>\mapsto{(x+10)=2(y+10)}↦(x+10)=2(y+10)</p><p></p><p>\mapsto{x+10=2y+20}↦x+10=2y+20</p><p></p><p>\mapsto{x=2y+20-10}↦x=2y+20−10</p><p></p><p>\mapsto{x=2y+10}↦x=2y+10 ..............(ii)</p><p></p><p>___________________________________</p><p></p><p>Substituting the value of x and find the age of y :</p><p></p><p>\mapsto{3y-2y-10=10}↦3y−2y−10=10</p><p></p><p>\mapsto{y=10+10}↦y=10+10</p><p></p><p>\mapsto{y=20\:years}↦y=20years</p><p></p><p>____________________________________</p><p></p><p>Now , find the age of x :</p><p></p><p>Taking the equation (ii)</p><p></p><p>\mapsto{x=2y+10}↦x=2y+10</p><p></p><p>\mapsto{x=(2×20)+10}↦x=(2×20)+10</p><p></p><p>\mapsto{x=40+10}↦x=40+10</p><p></p><p>\mapsto{x=50\:years}↦x=50years</p><p></p><p>So , the age of Pradeep and Vinay is 20 years and 50 years respectively.</p><p></p><p>▪︎ Additional information ▪︎</p><p></p><p>First equation of motion :</p><p></p><p>Vf = Vi + atVf=Vi+at</p><p></p><p>Where,</p><p></p><p>Vf = Final velocity</p><p></p><p>Vi = Initial velocity</p><p></p><p>a = Acceleration</p><p></p><p>t = Time taken</p><p></p><p>Second equation of motion:</p><p></p><p>s=ut+\frac{1}{2}at²s=ut+21at²</p><p></p><p>Where,</p><p></p><p>s = Distance travelled</p><p></p><p>u = Initial velocity</p><p></p><p>a = Acceleration</p><p></p><p>t = Time taken</p><p></p><p>Third equation of motion:</p><p></p><p>v²=u²+2aSv²=u²+2aS</p><p></p><p>Where,</p><p></p><p>v = Final velocity</p><p></p><p>u = Initial velocity</p><p></p><p>a = Acceleration</p><p></p><p>S = Displacement</p><p></p><p>$