Question

Ram is three times as old as Shyama .Four years ago his age was five times Shyama's age .find their present ages​

Answer 1

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:}Verification:

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

Forfirstcase:−

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.

{For\: second\: case :-}

Forsecondcase:−

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}=>15=15

LHS = RHS.

Hence verified.