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Let the initial quantities of alcohol and water be 3x and 2x liters, respectively. When 15 liters of water is added, the new ratio becomes 3:5: (3x) / (2x + 15) = 3/5 Cross-multiply: 5 × 3x = 3 × (2x + 15) 15x = 6x + 45 9x = 45 x = 5 Initial alcohol = 3x = 15 liters Correct answer: d) 15 liters
I: 2x² - 8x + 6 = 0
II: 3y² - 12y + 9 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 32x + 207 = 0
Equation 2: y² - 51y + 648 = 0
I. 15y2+ 26y + 8 = 0
II. 20x2+ 7x – 6 = 0
I. x2 + 11x + 30 = 0
II. y2 + 17y + 72 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 54x + 704 = 0
Equation 2: y² - 44y + 448 = 0
(i) x² – 3x – 40 = 0
(ii) y² + 11y + 30 = 0
I. 2x2 – 19x + 45 = 0
II. y2 – 14y + 48 = 0
I. p2 - 53p + 672 = 0
II. q2 - 27q + 126 = 0
I. 5x + y = 37
II. 4y+ x = 15
I. 2b2- 37b + 143 = 0
II. 2a2+ 15a - 143 = 0
