The ratio of the present ages of Ramita and Satyajit is 9:7. After 9 years, the ratio of their ages will become 5:4. What is Ramita's present age (in years)?

Introduction:This is a ratio-based ages problem where the ratio changes after a fixed number of years. The concept is that if present ages are in the ratio 9:7, we can represent them as 9x and 7x. After 9 years, we add 9 to both and use the new ratio 5:4 to solve for x. Once x is found, Ramita's present age is 9x.

Given Data / Assumptions:

• Present ratio Ramita : Satyajit = 9 : 7
• After 9 years, ratio becomes 5 : 4
• Let Ramita = 9x and Satyajit = 7x at present

Concept / Approach:Represent ages using a common factor x. Use the future ratio equation: (9x + 9)/(7x + 9) = 5/4 and solve for x.

Step-by-Step Solution:Let Ramita = 9x and Satyajit = 7xAfter 9 years: Ramita = 9x + 9, Satyajit = 7x + 9Given (9x + 9)/(7x + 9) = 5/4Cross-multiply: 4(9x + 9) = 5(7x + 9)36x + 36 = 35x + 45x = 9Ramita's present age = 9x = 9 * 9 = 81

Verification / Alternative check:If Ramita is 81 and Satyajit is 63, the present ratio is 81:63 = 9:7. After 9 years, they become 90 and 72, ratio 90:72 = 5:4. Both match, so 81 is correct.

Why Other Options Are Wrong:56 and 63: are based on the initial ratio but do not satisfy the second ratio after adding 9 years.80: close but breaks exact ratio conversion.72: would imply x=8, which fails the future ratio equation.

Common Pitfalls:Adding 9 years to only one person.Treating 9:7 as difference rather than a ratio multiplier.Solving for x but forgetting to multiply by 9 to get Ramita's age.

Final Answer:81 years