Setting Up Age Equations

Let R represent the age of Ram and Y represent the age of Ramya.

Translate the given information into algebraic equations:

• "2 times the age of Ram is 25 years more than 9 times the age of Ramya" translates to: $2R = 9Y + 25 \quad (1)$
• "5 times the age of Ramya is 4 years less than the age of Ram" translates to: $5Y = R - 4 \quad (2)$

Solving for Ram's Age (R) and Ramya's Age (Y)

We can use the substitution method. Rearrange Equation (2) to express R in terms of Y:

From Equation (2): $R = 5Y + 4$.

Now, substitute this expression for R into Equation (1):

$2(5Y + 4) = 9Y + 25$

Distribute the 2:

$10Y + 8 = 9Y + 25$

Solve for Y:

$10Y - 9Y = 25 - 8$

$Y = 17$

So, Ramya's age is 17 years.

Now substitute the value of Y back into the expression for R (from Equation 2):

$R = 5Y + 4$

$R = 5(17) + 4$

$R = 85 + 4$

$R = 89$

So, Ram's age is 89 years.

Calculating the Age Difference

The question asks for the difference between the ages of Ram and Ramya.

Difference = Ram's Age - Ramya's Age

Difference = $R - Y$

Difference = $89 - 17$

Difference = $72$ years.