Question

five years ago ram was twice as old as Shyam . fifteen years ago ram was four times as old as Shyam . find their present ages​

Answer 1

$\bf{\huge{\underline{\boxed{\sf{\red{Answer:}}}}}}$

$\bf{\underline{\sf{\purple{Given:}}}}$

• Five years ago ram was twice as old as Shyam
• Fifteen years ago ram was four times as old as Shyam

$\bf{\underline{\sf{\purple{To\:find:}}}}$

• Present age of Ram
• Present age of Shyam

$\bf{\underline{\sf{\purple{Solution:}}}}$

Let the present age of Ram be x years.

Let the present age of Shyam be y years.

$\bf{\underline{\sf{\purple{As\:per\:first\:condition:}}}}$

• Five years ago ram was twice as old as Shyam

Ages 5 years ago :-

Ram's age = x - 5 years

Shyam's age = y - 5 years

Representing mathematically,

=> x - 5 = 2 ( y - 5)

=> x - 5 = 2y - 10

=> x - 2y = - 10 + 5

=> x - 2y = - 5 -----> 1

$\bf{\underline{\sf{\purple{As\:per\:second\:condition:}}}}$

• Fifteen years ago ram was four times as old as Shyam

Ages 15 years ago :-

Ram's age = x - 15 years

Shyam's age = y - 15 years

Representing second condition mathematically,

=> x - 15 = 4 ( y - 15)

=> x -15 = 4y - 60

=> x - 4y = - 60 + 15

=> x - 4y = - 60 ----> 2

Solve equations 1 and 2 simultaneously by elimination method.

Subtract equation 2 from 1,

....+ x - 2y = - 5 -----> 1

- ( + x - 4y = - 45 ) -----> 2

________________________

2y = 40

y = $\sf\frac{40}{2}$

y = 20

Substitute y = 20 in equation 1,

x - 2y = - 5 ----> 1

x - 2 ( 20 ) = - 5

x - 40 = - 5

x = - 5 + 40

x = 35

•°• Present age of Ram = x = 35 years

Present age of Shyam = y = 20 years.

Answer 2

SOLUTION:-

Given:

⚫5 years ago Ram was twice as old as Shyam.&

⚫15 years ago ram was four times as old as Shyam.

Therefore,

Let the age of Shyam= x years

Let the age of Ram = y years.

So, 5 years ago:

Age of Shyam= (x-5) years

Age of Ram = (y-5) years.

As the Ram was twice times older than Shyam 5 years ago:

=) y-5 = 2(x-5)

=) y-5 = 2x-10

=) y -2x= -10+5

=) y -2x= -5....................(1)

Now,

15 years ago;

Age of Ram= (y-15)years

Age of Shyam= (x-15) years

So,

15 years ago, age of Ram will four times the age of Shyam:

=) y-15 = 4(x-15)

=) y-15 = 4x - 60

=) y - 4x = -60+15

=) y -4x = -45...............(2)

Therefore,

Subtracting equation (1) from (2), we get;

=) -2x= -40

=) x= 40/2 [Minus Cancel]

=) x= 20

Therefore,

Putting the value of x in equation (1), we get:

=) y -2(20)= -5

=) y - 40= -5

=) y= -5 +40

=) y= 35

Thus,

Present age of Ram,(y) = 35 years.

Present age of Shyam,(x)= 20 years.

Hope it helps ☺️