Let the present age of the father be F and the present age of the daughter be D. The present ratio of their ages is 3:1, so $\frac{F}{D} = \frac{3} {1}$. This gives us F = 3D (Equation 1). 4 years ago, the father's age was F-4 and the daughter's age was D-4. The ratio of their ages 4 years ago was 4:1, so $\frac{F-4}{D-4} = \frac{4}{1}$. This gives us F-4 = 4(D-4) (Equation 2). Now we solve the system of equations. Substitute Equation 1 into Equation 2: (3D) - 4 = 4(D - 4) 3D - 4 = 4D - 16 Add 16 to both sides and subtract 3D from both sides: 16 - 4 = 4D - 3D 12 = D The daughter's present age is 12 years. Substitute D=12 into Equation 1 to find the father's present age: F = 3 12 F = 36 The father's present age is 36 years. We need to find the average age of the father and daughter 2 years hence (which means 2 years from now). Father's age 2 years hence = F + 2 = 36 + 2 = 38 years. Daughter's age 2 years hence = D + 2 = 12 + 2 = 14 years. The sum of their ages 2 years hence = 38 + 14 = 52 years. The average age 2 years hence = $ \frac{\text{Sum of ages}}{\text{Number of people}} = \frac{52}{2} = 26$ years.
The ratio of the ages of father and the daughter at present is 3:1, 4 years ago the ratio was 4 : 1. The average age of the father and daughter 2 year hence will be?
Asked in GPSC Prelims CSP 1 2019 · Topic: Mechanics (Newton's Laws of Motion and their applications)
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