The sum of the ages of two persons is 60 years. In 5 years, the ratio of their ages will be 4:5. Find their present ages.

Let the present ages of the two persons be x and y. Then, we are given: x + y = 60 (Equation 1) In 5 years, their ages will be x + 5 and y + 5. We are also given that the ratio of their ages in 5 years is 4:5, so: (x + 5)/(y + 5) = 4/5 Cross multiply to get: 5(x + 5) = 4(y + 5) 5x + 25 = 4y + 20 5x - 4y = -5 (Equation 2) Now, solve the system of equations: From Equation 1: y = 60 - x Substitute into Equation 2: 5x - 4(60 - x) = -5 5x - 240 + 4x = -5 9x = 235 x = 235/9 ≈ 26.11 (rounded) So, x ≈ 26 years, and y ≈ 34 years (since x + y = 60). Thus, the ages are approximately 26 and 34 years. Correct Option: a) 26 years and 34 years