The sum of ages of Ram and Shyam is 32 years. Ram is older than Shyam by two years. Find their ages.
x+y=32
x-2=y
x+x-2=32
2x-2=32
2x=34
x=17
Ram is 17 years old and Shyam is 15.
Let's solve this step by step.
Step 1: Let's assume Ram's age as x years.
Step 2: Since Ram is older than Shyam by two years, Shyam's age can be expressed as (x - 2) years.
Step 3: The sum of their ages is given as 32 years. So, we can write the equation as:
x + (x - 2) = 32
Step 4: Combine like terms:
2x - 2 = 32
Step 5: Add 2 to both sides of the equation to isolate x:
2x - 2 + 2 = 32 + 2
2x = 34
Step 6: Divide both sides of the equation by 2 to solve for x:
2x/2 = 34/2
x = 17
Step 7: Now substitute the value of x back into the equation to find Shyam's age:
Shyam's age = x - 2
= 17 - 2
= 15
Step 8: Therefore, Ram's age is 17 years and Shyam's age is 15 years.
To find the ages of Ram and Shyam, we can use a system of equations.
Let's assume Ram's age as 'x' years and Shyam's age as 'y' years.
According to the given information:
1. The sum of their ages is 32: x + y = 32
2. Ram is older than Shyam by two years: x = y + 2
We have a system of two equations:
Equation 1: x + y = 32
Equation 2: x = y + 2
To solve this system of equations, we can use the method of substitution.
From Equation 2, we know that x = y + 2. We can substitute this value of x in Equation 1.
Substituting x = y + 2 in Equation 1:
(y + 2) + y = 32
2y + 2 = 32
2y = 32 - 2
2y = 30
y = 30 / 2
y = 15
Now, substitute the value of y back into Equation 2 to find x:
x = y + 2
x = 15 + 2
x = 17
Therefore, Ram is 17 years old and Shyam is 15 years old.