Question

The numerator of a rational number is less than its denominator by 4 .The numerator is multiplied by 2 and the denominator is increased by 4,the number becomes 14/15 find the original number

Answer 1

Question :

• The numerator of a rational number is less than its denominator by 4 .The numerator is multiplied by 2 and the denominator is increased by 4,the number becomes 14/15 find the original number.

Solution:

1. Let the Denominator be x
2. ⇒Numerator is x-4
3. Orignal no is $=\dfrac{x-4}{x}$

• According to the question:
• The numerator is multiplied by 2 and the denominator is increased by 4,the number becomes 14/15

$\sf \implies \dfrac{(x - 4) \times 2}{x + (4)} = \dfrac{14}{15}$

$\sf \implies \dfrac{2x - 8}{x + 4} = \dfrac{14}{15}$

• Now cross multiply the values

$\sf \implies(2x - 8)15 = 14(x + 4)$

$\sf \implies30x - 120 = 14x + 56$

$\sf \implies30x - 14x = 56 + 120$

$\sf \implies16x = 176$

$\sf \implies \:x = \dfrac{176}{16} = 11$

• Therefore , Original number is

$\sf \dfrac{x - 4}{x} = \dfrac{11 - 4}{11} = \dfrac{7}{11}$

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Verification :

when the original no :numerator is multiplied by 2 and the denominator is increased by 4,the number becomes 14/15

$\implies \sf \dfrac{7 \times 2}{11 + 4} = \dfrac{14}{15}$

Hence verified !!