Question
A vessel contains 100 litres of mixture (milk + water)
in which milk and water are in the ratio 5:5, respectively. If 30 litres of this mixture is taken out and replaced by 20 litres of water, then what would be the ratio of quantities of milk and water in the resulting mixture?Solution
ATQ, Initially, Quantity of milk in the mixture = 100 × (5/10) = 50 litres Quantity of water in the mixture = 100 × (5/10) = 50 litres Quantity of milk taken out = 30 × (5/10) = 15 litres Quantity of water taken out = 30 - 15 = 15 litres After removal and addition, Quantity of milk = 50 - 15 = 35 litres Quantity of water = 50 - 15 + 20 = 55 litres Ratio of quantity of milk to that of water = 35:55 = 7:11
I. 6y2 – 23y + 20 = 0
II. 4x2 – 24 x + 35 = 0
I. 117x² + 250x + 117 = 0
II. 54y² -123y + 65 = 0
The equation x2 – px – 60 = 0, has two roots ‘a’ and ‘b’ such that (a – b) = 17 and p > 0. If a series starts with ‘p’ such...
I. 3p² + 13p + 14 = 0
II. 8q² + 26q + 21 = 0
I. 6 y² + 11 y – 7= 0
II. 21 x² + 5 x – 6 = 0
I. x2 – 18x + 81 = 0
II. y2 – 3y - 28 = 0
I.8(x+3) +Â 8(-x) =72Â
II. 5(y + 5) + 5(-y) = 150Â
I. 22x² - 97x + 105 = 0
II. 35y² - 61y + 24 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 2x² - 8x + 6 = 0
Equation 2: y² - 7y + 10 = 0
I. 10x2 + 33x + 9 = 0
II. 2y2 + 13y + 21 = 0
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