Question
Tea worth Rs. 80/kg and Rs. 100/kg are mixed with a third
variety in the ratio 5:3:2 respectively. If the final mixture is worth Rs. 92/kg, then the price of the third variety of tea is:Solution
Let the quantity of three varieties of tea in the new mixture be ‘5x’ kg, ‘3x’ kg, and ‘2x’ kg respectively
Let the price of the third variety of tea be Rs. ‘y’/kg
ATQ:
(80 × 5x) + (100 × 3x) + (y × 2x) = 92 × (5x + 3x + 2x)
Or, 400x + 300x + 2xy = 92 × 10x
Or, 700x + 2xy = 920x
Or, 2xy = 220x
Or, y = 110
So, the price of the third variety of tea = Rs. 110/kg
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
Relevant for Exams:
