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A is as much younger than B as he is older than C. If the sum of the ages of B and C is 15 years, what is definitely the difference between B and A's age?
- a)1 year
- b)2 year
- c)25 year
- d)data inadequate
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A is as much younger than B as he is older than C. If the sum of the ...
B - A = B - C => A = C.
View all questions of this test
Also, B + C = 15 => B + A = 15
So, (B - A) cannot be determined.
Most Upvoted Answer
A is as much younger than B as he is older than C. If the sum of the ...
Given information:
- A is as much younger than B as he is older than C.
- Sum of ages of B and C is 15 years.
To find:
The definite difference between B and A's age.
Solution:
Let's assume that the age of C is x years.
According to the first given information, the age difference between A and B is equal to the age difference between A and C.
Hence, age of A - age of B = age of A - age of C
=> age of C = age of B - age of A
From the second given information, we know that the sum of ages of B and C is 15 years.
=> age of B + age of C = 15
=> age of B + (age of B - age of A) = 15 (using the above equation)
=> 2*age of B - age of A = 15
We have two equations:
- age of C = age of B - age of A
- 2*age of B - age of A = 15
We can solve these equations to find the values of A, B, and C. But the question asks for the definite difference between B and A's age, which we can find directly from the above equations.
Let's rearrange the second equation to get the value of age of A in terms of age of B:
=> age of A = 2*age of B - 15
Substituting this value in the first equation:
=> age of C = age of B - (2*age of B - 15)
=> age of C = 15 - age of B
Now, we can find the difference between B and A's age:
=> Difference = age of B - age of A
=> Difference = age of B - (2*age of B - 15)
=> Difference = 15 - age of B
Therefore, the definite difference between B and A's age is 15 - age of B.
We don't have enough information to find the value of age of B directly. Hence, the answer is (d) data inadequate.
- A is as much younger than B as he is older than C.
- Sum of ages of B and C is 15 years.
To find:
The definite difference between B and A's age.
Solution:
Let's assume that the age of C is x years.
According to the first given information, the age difference between A and B is equal to the age difference between A and C.
Hence, age of A - age of B = age of A - age of C
=> age of C = age of B - age of A
From the second given information, we know that the sum of ages of B and C is 15 years.
=> age of B + age of C = 15
=> age of B + (age of B - age of A) = 15 (using the above equation)
=> 2*age of B - age of A = 15
We have two equations:
- age of C = age of B - age of A
- 2*age of B - age of A = 15
We can solve these equations to find the values of A, B, and C. But the question asks for the definite difference between B and A's age, which we can find directly from the above equations.
Let's rearrange the second equation to get the value of age of A in terms of age of B:
=> age of A = 2*age of B - 15
Substituting this value in the first equation:
=> age of C = age of B - (2*age of B - 15)
=> age of C = 15 - age of B
Now, we can find the difference between B and A's age:
=> Difference = age of B - age of A
=> Difference = age of B - (2*age of B - 15)
=> Difference = 15 - age of B
Therefore, the definite difference between B and A's age is 15 - age of B.
We don't have enough information to find the value of age of B directly. Hence, the answer is (d) data inadequate.
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A is as much younger than B as he is older than C. If the sum of the ages of B and C is 15 years, what is definitely the difference between B and A's age?a)1 yearb)2 yearc)25 yeard)data inadequateCorrect answer is option 'D'. Can you explain this answer?
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