Rama’s age, 5 years hence, will be one year less than twice the age of Kapil at that time. Kapil’s age, 7 years hence, will be equal to (\frac{2}{3}) rd of Rama’s present age. What is the difference (in years) between the present ages of Rama and Kapil?

Let Rama's present age = R, Kapil's present age = K. First condition: R + 5 = 2(K + 5) - 1 = 2K + 9, so R - 2K = 4. Second condition: K + 7 = (2/3)R. From first equation: R = 2K + 4. Substituting in second: K + 7 = (2/3)(2K + 4) = (4K + 8)/3. Solving: 3K + 21 = 4K + 8, which gives K = 13 and R = 30. Difference R - K = 30 - 13 = 17 years.