Question
A tank has three pipes, X, Y, and Z. X can fill the tank
in 8 hours, Y can fill it in 12 hours, and Z can empty it in 6 hours. If X, Y, and Z are opened together, how long will it take to fill the tank?Solution
Work done by X in 1 hour = 1/8 Work done by Y in 1 hour = 1/12 Work done by Z in 1 hour (emptying) = -1/6 Net work in 1 hour = (1/8) + (1/12) - (1/6) Taking LCM of 8, 12, and 6 = 24, Net work = (3/24) + (2/24) - (4/24) = 1/24 The tank will be filled in 24 hours.
I. x2 - 5x - 14 = 0
II. y2 - 16y + 64 = 0
I. 22x² - 97x + 105 = 0
II. 35y² - 61y + 24 = 0
- If the quadratic equation x² + 18x + n = 0 has real and equal roots, what is the value of n?
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 27x² - 114x + 99 = 0
Equation 2: 18y² - 70y + 68 = 0
I. 56x² - 99x + 40 = 0
II. 8y² - 30y + 25 = 0
I). p2 - 26p + 165 = 0
II). q2 + 8q - 153 = 0
I. x2 + 91 = 20x
II. 10y2 - 29y + 21 = 0
In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between x and y.
I. x
I. 8x – 3y = 85
II. 4x – 5y = 67
I. 6x2 - 41x+13=0
II. 2y2 - 19y+42=0
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