Question
There are three numbers 'x', 'y' and 'z' (x < y < z)
such that 'y' is equal to the average of 'x' and 'z'. 40% of 'z' is equal to 'x' and the difference between 'y' and 'z' is 15. Find the sum of all three numbers.Solution
ATQ, 'y' = (1/2) × (x + z) Or, 2y = x + z And, 0.4z = 'x' Or, z = 5:2 Let 'z' = '5b' and 'x' = '2b' So, 2y = 2b + 5b Or, 'y' = (7b/2) Now, z - y = 15 Or, 5b - (7b/2) = 15 Or, (3b/2) = 15 Or, 'b' = 10 Required sum = 2b + {(7/2) × 10} + (5 × 10) = 20 + 35 + 50 = 105
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
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