Given data:
The sum of the present ages of Ram and Shyam is 36 years: Ram + Shyam = 36
Ram is elder than Shyam by 2 years: Ram = Shyam + 2
We have two equations and two variables, x (Ram's age) and y (Shyam's age). We can solve the system of equations to find their present ages.
Substitute the second equation into the first equation:
x + y = 36
Substitute Ram = Shyam + 2:
x = y + 2
Now we have a system of two equations:
x + y = 36
x = y + 2
We can solve this system of equations by substitution or elimination method. Let's use the substitution method.
From equation 2, we have x = y + 2.
Substitute this expression for x in equation 1:
(y + 2) + y = 36
Combine like terms:
2y + 2 = 36
Subtract 2 from both sides of the equation:
2y = 36 - 2
Simplify:
2y = 34
Divide both sides of the equation by 2:
y = 34/2
Simplify:
y = 17
Substitute y = 17 into equation 2 to find x:
x = y + 2 = 17 + 2 = 19
Therefore, Ram's present age (x) is 19 years and Shyam's present age (y) is 17 years.
