Question

numerator of a fraction is 4 less than its denominator. if we add 1 to the numerator and subtract 2 from the denominator it become 4/5. find the original fraction.​

Answer 1

Step-by-step explanation:

Let the numerator of the fraction be x and denominator be y.

According to the first condition:

x = y - 4...... (1)

According to the second condition:

$\frac{x + 1}{y - 2} = \frac{4}{5} \\ 5(x + 1) = 4(y - 2) \\ 5x + 5 = 4y - 8 \\ 5x = 4y - 8 - 5 \\ 5x = 4y - 13....(2) \\ from \: equations \: (1) \: and \: (2) \\ 5(y - 4) = 4y - 13 \\ 5y - 20 = 4y - 13 \\ 5y - 4y = 20 - 13 \\ y = 7 \implies \: x = 7 - 4 = 3 \\ thus \: x = 3 \: and \: y = 7 \\ hence \: the \: original \: fraction \: is \: \frac{3}{7} .$