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The denominator of a fraction is greater than the number by 8 if the number is 6 increased and denominator decreased by 2 then fraction become 1 find the fraction

Posted by Karan Pal 6 years, 6 months ago

CBSE > Class 08 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let the rational number be {tex}\frac{x}{{x + 8}}{/tex}
According to the question,
{tex}\frac{{x + 7}}{{x + 8 - 1}} = \frac{3}{2}{/tex}
∴ {tex}\frac{{x + 17}}{{x + 7}} = \frac{3}{2}{/tex}
∴ {tex}\frac{{x + 17}}{{x + 7}} \times (x + 7) = \frac{3}{2} \times (x + 7){/tex} . . . . [ Multiplying both sides x + 7, ]
∴ {tex}x + 17 = \frac{{3(x + 7)}}{2}{/tex}
2(x + 17) = 3(x + 7) . . . . [ Multiplying both sides 2 ]
∴ 2x + 34 = 3x + 21
∴ 34 – 21 = 3x – 2x . . . . [ Transposing 21 to L.H.S. and 2x to R.H.S. ]
∴ 13 = x
∴ x = 13
∴ x + 8 = 13 + 8 = 21 hence, the rational number {tex}\frac{{13}}{{21}},{/tex}
Verification
21 = 13 + 8
{tex}\frac{{13 + 7}}{{21 - 1}} = \frac{{30}}{{20}} = \frac{{30 \div 10}}{{20 \div 10}} = \frac{3}{2}{/tex} hence, the result is verified.

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CBSE > Class 08 > Mathematics