Question
Two inlet pipes M and N alone can fill a tank in 12
hours and 15 hours respectively and an outlet pipe P alone can empty the whole tank in 10 hours. First pipe M is opened for 4 hours, then pipe P is opened for 2 hours and rest of the tank is filled by pipe N. In what time will the tank be filled completely?Solution
Total capacity = 60 units (LCM of 12, 15 and 10) Efficiency of pipe M = 60/12 = 5 units/hr Efficiency of pipe N = 60/15 = 4 units/hr Efficiency of pipe P = 60/-10 = -6 units/hr Capacity of tank filled by pipe M in 4 hours = 5 × 4 = 20 units Capacity of tank emptied by pipe P in 2 hours = -6 × 2 = -12 units Capacity of tank left for pipe N = 60 – 20 – (-12) = 52 units Time taken by pipe N to fill the remaining tank = 52/4 = 13 hrs Total time taken = 4 + 2 + 13 = 19 hrs
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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