There are two sisters. If 1 is added to elder sister then the ratio of

1.	There are two sisters. If 1 is added to elder sister then the ratio of them is 0.5:1. If 2 is subtracted from younger sister then the ratio is 1:3. What is the ratio of them now?
Answer» Answer:- $\sf{<klux>RATIO</klux> \ of \ their \ present \ age \ is \ 7:15}$ Given: There are two sisters. If 1 is ADDED to elder sister then the ratio of them is 0.5:1 If 2 is subtracted from YOUNGER sister then the ratio is 1:3 To find: Ratio of present AGES of sisters. Solution: $\sf{Let \ the \ age \ of \ younger \ sister \ be \ y \ years \ and}$ $\sf{age \ of \ elder \ sister \ be \ x \ years \ respectively.}$ $\sf{According \ to \ the \ first \ condition.}$ $\sf{\frac{y}{x+1}=\frac{0.5}{1}}$ $\sf{\therefore{=0.5(x+1)}}$ $\sf{Multiply \ both \ sides \ by \ 2, \ we \ get}$ $\sf{2y+2=x+1...(1)}$ $\sf{According \ to \ the \ second \ condition.}$ $\sf{\frac{y-2}{x}=\frac{1}{3}}$ $\sf{\therefore{x=3(y-2)}}$ $\sf{\therefore{x=3y-6...(2)}}$ $\sf{Substitute \ equation (2) \ in \ equation (1)}$ $\sf{2y+2=3y-6+1}$ $\sf{\therefore{3y-2y=5+2}}$ $\boxed{\sf{\therefore{y=7}}}$ $\sf{Substitute \ y=7 \ in \ equation (2), \ we \ get}$ $\sf{x=3(7)-6}$ $\sf{\therefore{x=21-6}}$ $\boxed{\sf{\therefore{x=15}}}$ $\sf{Ratio \ of \ their \ present \ ages \ is}$ $\sf{\frac{y}{x}=\frac{7}{15}}$ $\sf\purple{\tt{\therefore{Ratio \ of \ their \ present \ ages \ is \ 7:15}}}$