Q32 (CISF/2025) Science & Technology › Basic Science (Physics, Chemistry, Biology)

The present age of A is the square of the present age of B. One year back, the sum of squares of their ages is two years more than the product of their present ages. The present ages of A and B (in years) are, respectively :

Explanation

Let the present age of B be x years. According to the problem, the present age of A is x² years.

One year ago, their ages were (x² - 1) and (x - 1). The problem states that the sum of the squares of these ages was two more than the product of their present ages:
(x² - 1)² + (x - 1)² = (x² × x) + 2

Expanding the equation:
(x⁴ - 2x² + 1) + (x² - 2x + 1) = x³ + 2
x⁴ - x² - 2x + 2 = x³ + 2
x⁴ - x³ - x² - 2x = 0

Dividing by x (since age x ≠ 0):
x³ - x² - x - 2 = 0

Testing Option B (where B = 2):
2³ - 2² - 2 - 2 = 8 - 4 - 2 - 2 = 0. This satisfies the equation. Thus, B's age is 2 and A's age is 2² = 4.

Change set

Question map

The present age of A is the square of the present age of B. One year back, the sum of squares of their ages is two years more than the product of their present ages. The present ages of A and B (in years) are, respectively :

Explanation

SIMILAR QUESTIONS

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