Algebra
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Q.

If 1 added to the age of the elder sister, then the ratio of the ages of two sisters becomes $0.5 : 1$, but if 2 is subtracted from the age of the younger one, the ratio becomes $1:3$, the age of the younger sister will be?

 A.

7 year

 B.

5 year

 C.

8 year

 D.

10 year

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Solution:
Option(B) is correct

Suppose that age of elder sister be $x$ year, and younger sister be $y$ year. Then:

\(\dfrac{y}{x+1}=\dfrac{0.5}{1}=\dfrac{1}{2}\)

\(\Rightarrow x-2y=-1\)-------(i)

Again given: 

\(\dfrac{y-2}{x}=\dfrac{1}{3}\)

\(\Rightarrow x-3y=-6\)-------- (ii)

From both the equations we get:

$x=9$ and $y=5$

So, the age of younger sister is 5 years


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