If two is added to the denominator of a rational number it becomes 1 and if 4 is added to the numerator it becomes ½. Then the sum of the numerator and the denominator of the rational number is:
Let the rational number be x/y. When 2 is added to the denominator, => x/(y + 2) = 1 ⇒ x = y + 2 ⇒ y = x – 2 ------ (i) When 4 is added to the numerator, => (x + 4)/y = 1/2 ⇒ 2x + 8 = y ------- (ii) Solving equation eq. (i) and (ii) we get, => x – 2 = 2x + 8 ⇒ x = -10 Putting the value of ‘x’ in equation (i) we get, => y = -10 - 2 ⇒ y = -12 Required sum = -10 + (-12) = -22
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