Question
In a container, the ratio of milk to water is 5:3. If
30% of the mixture is removed and replaced by the same quantity of milk and 24 ml of water is added afterwards, the new ratio of milk to water becomes 11:5. What was the volume of the mixture removed?Solution
ATQ,
Let the quantities of milk and water be 5x ml and 3x ml respectively Amount of mixture taken out = 0.3 × (5x + 3x) = 2.4x According to question, (0.7 × 5x + 2.4x)/(0.7 × 3x + 24) = 11/5 (3.5x + 2.4x)/(2.1x + 24) = 11/5 5.9x/(2.1x + 24) = 11/5 Cross-multiplying: 5 × 5.9x = 11 × (2.1x + 24) 29.5x = 23.1x + 264 6.4x = 264 x = 41.25 Amount of mixture taken out = 2.4 × 41.25 = 99 ml
I. 15y2 + 26y + 8 = 0
II. 20x2 + 7x – 6 = 0
I. x2 – 10x + 21 = 0
II. y2 + 11y + 28 = 0
- If the quadratic equation x² + 18x + n = 0 has real and equal roots, what is the value of n?
I. 35x² - 24x – 35 = 0
II. 72y² - 145y + 72 = 0
I. 2x2 – 5x – 12 = 0
II. 2y2 + 13y + 20 = 0
I. 22x² - 97x + 105 = 0
II. 35y² - 61y + 24 = 0
I. 4x2 + 3√7 x-7 =0
II. 7y2 + 4√7 y-5=0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 11x² - 93x + 88 = 0
Equation 2: 13y² + 118y + 93 = 0
I. 5x² - 28x + 39 = 0
II. 2y² - 13y + 20 = 0
I. 4x2 + 9x - 9 = 0
II. 4y2 - 19y + 12 = 0
Relevant for Exams:
