Question

when one is added to each of two numbers their ratio becomes 1:2 and when subtracted 5 from each of them the number becomes 5:11. find the no.​

Answer 1

$let \: the \: number \: is \frac{x}{y} \\ \frac{x + 1}{y + 1} = \frac{1}{2} \\ 2x + 2 = y + 1 \\ 2x + 1 = y \\ now \: the \: second \: equation \: \\ \frac{x - 5}{y - 5} = \frac{5}{11} \\ 11x - 55 = 5y - 25 \\ 11x - 30 = 5(2x + 1) = 10x + 5 \\ x = 30 + 5 = 35 y = 2x+1= 71$