Question
Two pipes, P and Q, can fill a tank in 60 minutes and 100
minutes, respectively. A third pipe R can empty it in 1 hour 40 minutes. Initially, pipes P and R are opened. After 30 minutes, pipe Q is also opened. How long will it take to completely fill the tank?Solution
ATQ,
Let the tank's capacity be 300 litres (LCM of 60, 100 and 100)
Efficiency of P = 300 ÷ 60 = 5 litres/minute
Efficiency of Q = 300 ÷ 100 = 3 litres/minute
Efficiency of R = 300 ÷ 100 = -3 litres/minute
Tank filled in 30 minutes = (5 - 3) × 30 = 60 litres
Remaining volume = 300 - 60 = 240 litres
Time to fill remaining = 240 ÷ (5 + 3 - 3) = 240 ÷ 5 = 48 minutes
Total time taken = 30 + 48 = 78 minutes
For 3x² − 10x − 8 = 0, find (1/α + 1/β).
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. 3x<...
I. 2x2 - 9 x + 9 = 0Â
II. 2y2 - 7 y + 3 = 0
I. 8x² - 74x + 165 = 0
II. 15y² - 38y + 24 = 0
I. 3x2 - 16x - 12 = 0
II. 2y2 + 11y + 9 = 0
In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between 'p' and 'q' and choose...
For what values of k does the equation x² – (k+1)x + k = 0 have two distinct real roots, both greater than 1?
l. x2 - 16x + 64 = 0
II. y2Â = 64
I. 66x² - 49x + 9 = 0
II. 46y² - 37y - 30 = 0
I. 3p² - 17p + 22 = 0
II. 5q² - 21q + 22 = 0
Relevant for Exams:
