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Question

# Five years ago, Shikha was thrice as old as Rani 10 years later, Shikha will be twice as old as Rani. How old are they now?

A
shikha 50, rani 20
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B
rani 20, shikha 50
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C
rani 30, shikha 80
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D
none
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Solution

## The correct option is B shikha 50, rani 20Let the present age of Shikha =x yearsLet the present age of Rani =y yearsFive years ago, Shikha was thrice as old as Rani.Five years ago, Shikha's age =x−5 yearsFive years ago, Rani's age =y−5 yearsx−5=3(y−5)x−5=3y−15x−3y−5+15=0x−3y+10=0 ............ (1)10 years later, Shikha will be twice as old as Rani.10 years later, Shikha's age =x+10 years10 years later, Rani's age =y+10 yearsx+10=2(y+10)x+10=2y+20x−2y+10−20=0x−2y−10=0 ............ (2)Subtracting equation (2) from (1), we get,x−3y+10−(x−2y−10)=0x−3y+10−x+2y+10=0−y+20=0y=20From equation (1),x−3y+10=0x−3(20)+10=0x−50=0x=50present age of Shikha =x=50 yearspresent age of Rani =y=20 years

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