Question

The numerator of a fraction is 9 less than the denominator. If 2 is subtracted from both numerator and
denominator, fraction becomes
Find the fraction became2/5 .find the fraction​

Answer 1

Step-by-step explanation:

Let the numerator be x

and denominator be y

According to the given information:

x = y - 9....... (1)

By second condition:

$\frac{x - 2}{y - 2} = \frac{2}{5} \\ x - 2 = \frac{2}{5} \times (y - 2) \\ x = \frac{2}{5}y - \frac{4}{5} + 2 \\ x = \frac{2y}{5} + \frac{10 - 4}{5} \\ x = \frac{2y}{5} + \frac{6}{5}.....(2) \\ from \: (1) \: and \: (2) \\ y - 9 = \frac{2y}{5} + \frac{6}{5} \\ y - \frac{2y}{5} = \frac{6}{5} + 9 \\ \frac{5y - 2y}{5} = \frac{6 + 45}{5} \\ 3y = 51 \\ y = \frac{51}{3} \\ y = 17 \\ x = 17 - 9 \\ x = 8 \\ thus \: the \: required \: fraction \: is \: \frac{8}{17} .$

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