the denominator of a rational number is greater than it's numerator by 8. if the numerator is increased by 17 and the denominator is decreased by 1.,the number obtained is 3/2. find the rational number.
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Let both of the numerator and denominator be x. Hence, we can write as => x/ x + 8 (as denominator is 8 more than the numerator.
Thus, => (x + 17) / ( x + 8 - 1) = 3 / 2
=> (x + 17) / (x + 7) = 3 / 2
If we cross multiply, it becomes -
=> 2x + 34 = 3 (x + 7)
=> 2x + 34 = 3x + 21
=> 34 - 21 = 3x - 2x
=> 13 = x
Thus, x = 13
As the denominator is 8 more than the numerator and x / x + 8, the answer is
=> 13 / 13 + 8 = 13 / 21
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