Question
The numerator of a fraction is 2 less than its
denominator. If the numerator is decreased by 2 and the denominator is increased by 3, the denominator becomes eight times the numerator. Find the fraction?Solution
Let the required fraction is x/y ATQ: x = y - 2 x - y = -2 ....(i) Also given, y + 3 = 8(x-2) ⇒ y + 3 = 8x – 16 ⇒ 8x – y = 16 + 3 ⇒ 8x – y = 19 …… (ii) Subtracting equation (ii) from (i), we get (x – y) – (8x – y) = – 2 – 19 ⇒ x – y − 8x + y = −21 ⇒ −7x = −21 ⇒ x = 21/7 = 3 Substituting the value of x = 3 in the equation (i) we find y 3 – y = – 2 ⇒ y = 3 + 2 ⇒ y = 5 Therefore, the fraction is 3/5.
I. 3p2 - 11p + 10 = 0
II. 42q2 + q -1 = 0
I). p2 + 22p + 72 = 0,
II). q2 - 24q + 128 = 0
Find the roots of the equation 6p² – 5p – 6 = 0.
I. y² + y – 56 = 0
II. 2x² + 11 x – 40 = 0
If x satisfies x² – 14x + 40 = 0, find x.
I. 2y² - 35y + 132 = 0
II. 2x² - 31x + 110 = 0
I. 35x² - 46x – 16 = 0
II. 35y² - 116y + 96 = 0
I. 20x² - 93x + 108 = 0
II.72y² - 47y - 144 = 0
I. x3 = 1728
II. y2 – 15y + 56 = 0
I. x2 + x – 42 = 0
II. y2 + 6y – 27 = 0
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