Question

ram is twice as old as shyam. five year ago ram was three times shyam 's age . find their present ages

Answer 1

hye

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let ram be r and shyam be s

Ram is twice as old as shyam


=> r = 2s

five year ago ram was three times shyam 's age  

=>lets form an equation

=>${r-5= 3}[s-5]$

we now that r is 2s

lets put it into the equation

=>${2s-5= 3}[s-5]$

=>
$2s - 5 = 3s -15$

=>2s -3s = +5 - 15

=>-s =-10

=>s = 10


ram = 2s

         = 2 *10

             =20 years

present age = >ram =  20 and shyam is 10 
        
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hope it helps uu...................

Answer 2

$\huge{\sf{\boxed{\boxed{Answer:}}}}$

Given that :

Ram is twice as old as Shyam.

Five years ago his age was three times of Shyam's age.

To find:

Present age of Ram.

Present age of Shyam.

Solution:

Let the present age of Ram be x years

Let the present age of Shyam be y years.

As per second condition :-

Ram is twice as old as Shyam

Representing mathematically,

x = 2y ---> 1

As per second condition:-

five years ago his age was three times of Shyam's age.

Ages 5 years ago :-

Ram's age = x - 5 years

Shyam's age = y - 5 years

Representing the second condition mathematically,

x - 5 = 3 ( y - 5)

x - 5 = 3y - 15

x - 3y = - 15 + 5

x - 3y = - 10 -----> 2

Substitute value of x in equation 2,

2y - 3y = - 10

- y = - 10

y = 10

Substitute value of y in equation 1,

x = 2y ---> 1

x = 2 ( 10)

x = 20

•°• Present age of Ram = x = 20 years.

Present age of Shyam = y = 10 years

$\huge\bold{Verification:}$

$\boxed{For\:first\:case :-}$

Ram is twice as old as Shyam

Present age of Ram = x = 20 years

Present age of Shyam = y = 10 years

=> x = 2y

=> 20 = 2 (10)

=> 20 = 20

LHS = RHS.

$\boxed{For\: second\: case :-}$

Five years ago his age was three times of Shyam's age

Ages 5 years ago :-

Ram's age = x - 5 = 20 - 5 = 15 years

Shyam's age = y - 5 = 10 - 5 = 5 years

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

=> 15 = 3 ( 5 )

$\bold{=> 15 = 15}$

LHS = RHS.

Hence verified.