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The Numerator of a Fraction is 5 Less than Its Denominator. If 3 is Added to the Numerator, and Denominator Both, the Fraction Becomes \\Frac{2}{3}\. Find the Original Fraction. - Mathematics

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Sum

The numerator of a fraction is 5 less than its denominator. If 3 is added to the numerator, and denominator both, the fraction becomes \[\frac{2}{3}\]. Find the original fraction.

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Solution

Let denominator of the original fraction = x

Then numerator = x – 5

and fraction = `("x" - 5)/"x"`

According to the condition,

`("x" - 5 + 3)/("x" + 3) = 4/5`

`=> ("x" - 2)/("x" + 3) = 4/5`

⇒ 5(x - 2) = 4x + 12

⇒ 5x - 10 = 4x + 12

⇒ x = 22

∴ Original fraction = `("x" - 5)/"x"`

`= (22 - 5)/22 = 17/22` 

Concept: Solving Linear Inequations
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APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 14 Linear Equations in one Variable
Exercise 14 (C) | Q 10 | Page 170
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