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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