Question
The ratio of the present age of A to that of B is 7:9.
Six years ago the ratio of 1/3 of A’s age at that time and 1/3 of B’s age at that time was 1:3. What will be the ratio of A’s age to B’s age 5 years from now?Solution
Let the present age of A and B be 7x and 9x respectively. Now, [(1/3) (7x-6)] / [(1/3) (9x-6)] = 1/3 ⇒ 21x – 18 = 9x – 6 ⇒ 12x = 12  ∴ x = 1 ∴ 5 years from now, A’s age = 7x + 5 = 7 + 5 = 12 years B’s age = 9x + 5 = 14 years ∴ Required ratio = 12/14 = 6:7
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 97x² - 436x + 339 = 0
Equation 2: 103y² - 460y + 357 = 0
If the roots of the quadratic equation 5x² + 4x + 6 = 0 are α and β, then what is the value of [(1/α) + (1/β)]?
...l). 3p + 2q = 27
ll). 4p - 3q = 2
I. p2 +7p + 10 = 0 II. q2 - q – 6 = 0
l). 2p² + 12p + 18 = 0Â
ll). 3q² + 13q + 12 = 0
I. x2 + 16x + 63 = 0
II. y2 + 2y - 15 = 0
I. p2 – 2p – 15 = 0
II. q2 + 4q – 12 = 0
I. 12a2 – 55a + 63 = 0
II. 8b2 - 50 b + 77 = 0
...I: x2Â + 31x + 228 = 0
II: y2 + 3y – 108 = 0
I. 7x² + 52x + 21 = 0
II. 6y² + 7y - 24 = 0
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