Question

If the numerator of a fraction is increased by 2
and denominator is decreased by 1, it
becomes. If the numerator is increased by 1
and denominator is increased by 2, it becomes
Find the fraction.
3​

Answer 1

Fraction\:is\: \frac{8}{15} \\ \\  

Solution:

Let the fraction is

\frac{x}{y} \\ \\  

according to the question,

\frac{x + 2}{y + 1} = \frac{5}{8} \\ \\ \\ 8(x + 2) = 5(y + 1) \\ \\ 8x + 16 = 5y + 5 \\ \\ 8x - 5y = - 11....eq1 \\ \\  

now another statement is

\frac{x - 1}{y - 1} = \frac{1}{2} \\ \\ 2(x - 1) = y - 1 \\ \\ 2x - 2 - y = - 1 \\ \\ 2x - y = 1....eq2 \\ \\  

Now solve equations 1 and 2

multiply eq2 by 4

8x - 5y = - 11 \\ 8x - 4y = 4 \\ - \: \: \: + \: \: \: \: \: \: - \\ - - - - - \\ - y = - 15 \\ \\ y = 15 \\ \\  

put the value of y in eq2

2x - y = 1 \\ \\ 2x - 15 = 1 \\ \\ 2x = 16 \\ \\ x = 8 \\ \\  

So the fraction is

\frac{8}{15} \\ \\  

Hope it helps you.