Rohit was 4 times as old as his son 8 years ago. After 8 years, Rohit will be twice as old as his son. What are theirpresent ages?
- Let son's age 8 years ago be x years. Then, Rohit's age 8 years ago = 4x years.
Son's age after 8 years = (x + 8) + 8 = (x + 16) years.
Rohit's age after 8 years = (4x + 8) + 8 = (4x+ 16) years.
2 (x + 16) = 4x + 16
2x = 16
x = 8.
Hence, son's 'present age = (x + 8) = 16 years.
Rohit'spresent age = (4x + 8) = 40 years.
Let the present age of Rohit be "R" and his son be "S".
According to the problem statement, we can form two equations:
Equation 1: R - 8 = 4(S - 8) (Rohit was 4 times as old as his son 8 years ago)
Equation 2: R + 8 = 2(S + 8) (After 8 years, Rohit will be twice as old as his son)
We need to solve these two equations to find the present ages of Rohit and his son.
Solving Equation 1 for R, we get:
R - 8 = 4S - 32
R = 4S - 24
Substituting this value of R in Equation 2, we get:
4S - 24 + 8 = 2S + 16
Simplifying this equation, we get:
2S = 32
S = 16
So, the present age of Rohit's son is 16 years.
Substituting this value of S in Equation 1, we get:
R - 8 = 4(16 - 8)
R - 8 = 32
R = 40
So, the present age of Rohit is 40 years.
Therefore, Option D (40 years) is the correct answer.
Some important formulas that we have used in this problem are:
If a person's present age is "P", and "N" years ago their age was "A", then we can write: P = A + N
If a person's present age is "P", and "N" years from now their age will be "B", then we can write: B = P + N
If two people's ages are "A" and "B", and one person is "X" times as old as the other, then we can write: A = X * B
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