Question

21. The numerator of a fraction is 1 less than the denominator. If
numerator is decreased by 2 and denominator is increased by 3,
the fraction becomes 1
4
. Find the original fraction.

Answer 1

Answer:

$\frac{4}{5}$

Step-by-step explanation:

let the denominator of the fraction be x

numerator will be (x-1)

fraction =

$\frac{x - 1}{x}$

if numerator decreased by 2 and denominator increased by 3 fraction will be equal to 1/4

$\frac{x - 1 - 2}{x + 3} = \frac{1}{4} \\ \\ \frac{x - 3}{x + 3} = \frac{1}{4}$

cross multiply

$4(x - 3) = 1(x + 3) \\ \\ 4x - 12 = x + 3 \\ \\ 4x - x = 3 + 12 \\ \\ 3x = 15 \\ \\ x = 15 \div 3 \\ \\ x = 5$

put the value of x

$\frac{x - 1}{x } \\ \frac{5 - 1}{5} \\ \frac{4}{5}$