Question

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 1

Answer:-

$\sf{Ratio \ of \ their \ present \ age \ is \ 7:15}$

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:

$\sf{Let \ the \ age \ of \ younger \ sister \ be \ y \ years \ and}$

$\sf{age \ of \ elder \ sister \ be \ x \ years \ respectively.}$

$\sf{According \ to \ the \ first \ condition.}$

$\sf{\frac{y}{x+1}=\frac{0.5}{1}}$

$\sf{\therefore{=0.5(x+1)}}$

$\sf{Multiply \ both \ sides \ by \ 2, \ we \ get}$

$\sf{2y+2=x+1...(1)}$

$\sf{According \ to \ the \ second \ condition.}$

$\sf{\frac{y-2}{x}=\frac{1}{3}}$

$\sf{\therefore{x=3(y-2)}}$

$\sf{\therefore{x=3y-6...(2)}}$

$\sf{Substitute \ equation (2) \ in \ equation (1)}$

$\sf{2y+2=3y-6+1}$

$\sf{\therefore{3y-2y=5+2}}$

$\boxed{\sf{\therefore{y=7}}}$

$\sf{Substitute \ y=7 \ in \ equation (2), \ we \ get}$

$\sf{x=3(7)-6}$

$\sf{\therefore{x=21-6}}$

$\boxed{\sf{\therefore{x=15}}}$

$\sf{Ratio \ of \ their \ present \ ages \ is}$

$\sf{\frac{y}{x}=\frac{7}{15}}$

$\sf\purple{\tt{\therefore{Ratio \ of \ their \ present \ ages \ is \ 7:15}}}$