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Q22
(CAPF/2024)
Miscellaneous & General Knowledge › Important Days, Places & Events › Important Days, Places & Events
The sum of the ages of A and B (in years) is 22. The product of their ages two years back was 77. Which one of the following is the value of the difference of their current ages?
Result
Your answer:
—
·
Correct:
C
Explanation
Let the current ages of A and B be A and B.
- Sum of their ages: A + B = 22
- Product of their ages two years ago: (A - 2) × (B - 2) = 77
Expanding the second equation:
AB - 2A - 2B + 4 = 77
AB - 2(A + B) + 4 = 77
Substitute A + B = 22 into the equation:
AB - 2(22) + 4 = 77
AB - 44 + 4 = 77
AB - 40 = 77
AB = 117
Now, use the algebraic identity to find the difference between their ages:
(A - B)² = (A + B)² - 4AB
(A - B)² = (22)² - 4(117)
(A - B)² = 484 - 468
(A - B)² = 16
Taking the square root gives |A - B| = 4. The difference in their current ages is 4 years.
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