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The brother is elder to his sister by 7 years. Five years ago, the product of their ages was 30, what is the present age of the brother?
- a)15 years
- b)8 years
- c)10 years
- d)3 years
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The brother is elder to his sister by 7 years.Five years ago, the prod...
Let the present age of sister be x
Present age of brother = x + 7
Sister’s age 5 years ago = x – 5
Brother’s age 5 years ago = x + 2
⇒ (x – 5)(x + 2) = 30
⇒ x2 – 3x – 10 = 30
⇒ x2 – 3x – 40 = 0
⇒ (x – 8)(x + 5) = 0
⇒ x = 8
∴ Present age of brother = 8 + 7 = 15 years
Present age of brother = x + 7
Sister’s age 5 years ago = x – 5
Brother’s age 5 years ago = x + 2
⇒ (x – 5)(x + 2) = 30
⇒ x2 – 3x – 10 = 30
⇒ x2 – 3x – 40 = 0
⇒ (x – 8)(x + 5) = 0
⇒ x = 8
∴ Present age of brother = 8 + 7 = 15 years
Most Upvoted Answer
The brother is elder to his sister by 7 years.Five years ago, the prod...
Given:
The brother is elder to his sister by 7 years.
Five years ago:
Let's assume the present age of the brother is B and the present age of the sister is S.
So, five years ago, the age of the brother was B-5 and the age of the sister was S-5.
Product of their ages:
Five years ago, the product of their ages was 30.
So, (B-5)(S-5) = 30
Equation:
We are given that the brother is elder to his sister by 7 years.
So, B = S + 7
Solving the equation:
Substituting B = S + 7 in the equation (B-5)(S-5) = 30, we get:
(S + 7 - 5)(S - 5) = 30
(S + 2)(S - 5) = 30
S^2 - 3S - 40 = 0
Factoring the equation:
(S - 8)(S + 5) = 0
So, S = 8 or S = -5
Since age cannot be negative, we discard S = -5.
Calculating the present age of the brother:
If S = 8, then B = S + 7 = 8 + 7 = 15
Therefore, the present age of the brother is 15 years, which corresponds to option A.
The brother is elder to his sister by 7 years.
Five years ago:
Let's assume the present age of the brother is B and the present age of the sister is S.
So, five years ago, the age of the brother was B-5 and the age of the sister was S-5.
Product of their ages:
Five years ago, the product of their ages was 30.
So, (B-5)(S-5) = 30
Equation:
We are given that the brother is elder to his sister by 7 years.
So, B = S + 7
Solving the equation:
Substituting B = S + 7 in the equation (B-5)(S-5) = 30, we get:
(S + 7 - 5)(S - 5) = 30
(S + 2)(S - 5) = 30
S^2 - 3S - 40 = 0
Factoring the equation:
(S - 8)(S + 5) = 0
So, S = 8 or S = -5
Since age cannot be negative, we discard S = -5.
Calculating the present age of the brother:
If S = 8, then B = S + 7 = 8 + 7 = 15
Therefore, the present age of the brother is 15 years, which corresponds to option A.
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The brother is elder to his sister by 7 years.Five years ago, the product of their ages was 30, what is the present age of the brother?a)15 yearsb)8 yearsc)10 yearsd)3 yearsCorrect answer is option 'A'. Can you explain this answer?
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