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Joes age , Joes sisters age and Joes fathers age sums up to a century. When sons as old as his father, Joes sister will be twice as old as now. When Joe is as old as his father then his father is twice as old as when his sister was as old as her father
- a)Joe=20 sister=30 father=50
- b)Joe=30 sister=20 father=50
- c)Joe=50 sister=30 father=20
- d)Joe=20 sister=50 father=30
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Joes age , Joes sisters age and Joes fathers age sums up to a century....
Let's break down the given information and solve the problem step by step:
1. Joe's age, Joe's sister's age, and Joe's father's age sum up to a century.
- Let's assume Joe's age as J, Joe's sister's age as S, and Joe's father's age as F.
- We can write the equation: J + S + F = 100 ...(Equation 1)
2. When Joe's son is as old as his father, Joe's sister will be twice as old as now.
- This means when Joe's son is F years old, Joe's sister will be 2S years old.
- We can write the equation: F + F = 2S ...(Equation 2)
3. When Joe is as old as his father, then his father is twice as old as when his sister was as old as her father.
- This means when Joe is F years old, his father will be 2(F - S) years old.
- We can write the equation: J + 2(F - S) = F ...(Equation 3)
Now, let's solve the equations:
From Equation 2, we can simplify it to:
2F = 2S
F = S ...(Equation 4)
Substitute Equation 4 into Equation 3:
J + 2(F - S) = F
J + 2(0) = F (Substituting F = S)
J = F
Substitute Equation 4 into Equation 1:
J + S + F = 100
J + J + J = 100 (Substituting F = S)
3J = 100
J = 100/3
J ≈ 33.33
Since Joe's age is given as a whole number, let's assume Joe is 33 years old.
Substitute J = 33 into Equation 4:
F = S = 33
Hence, Joe is 33 years old, Joe's sister is 33 years old, and Joe's father is 33 years old.
The given answer option 'A' (Joe=20, sister=30, father=50) does not satisfy any of the equations, so it is incorrect.
1. Joe's age, Joe's sister's age, and Joe's father's age sum up to a century.
- Let's assume Joe's age as J, Joe's sister's age as S, and Joe's father's age as F.
- We can write the equation: J + S + F = 100 ...(Equation 1)
2. When Joe's son is as old as his father, Joe's sister will be twice as old as now.
- This means when Joe's son is F years old, Joe's sister will be 2S years old.
- We can write the equation: F + F = 2S ...(Equation 2)
3. When Joe is as old as his father, then his father is twice as old as when his sister was as old as her father.
- This means when Joe is F years old, his father will be 2(F - S) years old.
- We can write the equation: J + 2(F - S) = F ...(Equation 3)
Now, let's solve the equations:
From Equation 2, we can simplify it to:
2F = 2S
F = S ...(Equation 4)
Substitute Equation 4 into Equation 3:
J + 2(F - S) = F
J + 2(0) = F (Substituting F = S)
J = F
Substitute Equation 4 into Equation 1:
J + S + F = 100
J + J + J = 100 (Substituting F = S)
3J = 100
J = 100/3
J ≈ 33.33
Since Joe's age is given as a whole number, let's assume Joe is 33 years old.
Substitute J = 33 into Equation 4:
F = S = 33
Hence, Joe is 33 years old, Joe's sister is 33 years old, and Joe's father is 33 years old.
The given answer option 'A' (Joe=20, sister=30, father=50) does not satisfy any of the equations, so it is incorrect.
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