Question

2) Nikita's present age is three times the present age of Nikhil. After 4 years the ratio of Nikita's age to Nikhil's age
will be 7: 3. Find their present ages.​

Answer 1

Step-by-step explanation:

$\sf{\bold{\blue{\underline{\underline{Given}}}}}$

●Nikita's present age is three times the present age of Nikhil.

●After 4 years the ratio of Nikita's age to Nikhil's age will be 7: 3.

$\sf{\bold{\red{\underline{\underline{To\:Find}}}}}$

Present age of nikhil and nikita?$\sf{\bold{\purple{\underline{\underline{Solution}}}}}$

$\longrightarrow$ If Nikhils present age =x

$\longrightarrow$so,Nikita's present age=3x⠀⠀⠀⠀

$\bold{\underline{after~ 4 ~years} }$ 

$\hookrightarrow$ Nikhils age=$\tt{ x+4  }$ 

$\hookrightarrow$ Nikita's age=$\tt{ 3x+4  }$      

According to the question,

After 4 years the ratio of Nikita's age to Nikhil's age will be 7: 3.

so,

$\rightsquigarrow$ $\tt{\dfrac{3x+4}{x+4}=\dfrac{7}{3}   }$    

$\rightsquigarrow$ $\tt{ 3(3x+4)=7(x+4)  }$      

$\rightsquigarrow$ $\tt{9x+12=7x-28}$      

$\rightsquigarrow$ $\tt{ 9x-7x=28-12  }$      

$\rightsquigarrow$ $\tt{2x=16   }$   

$\rightsquigarrow$ $\tt{x=\dfrac{16}{2}   }$   

$\rightsquigarrow$ $\tt{ x=\dfrac{\cancel{16}}{\cancel{2}}   }$     

$\rightsquigarrow$ $\bold{x=8   }$      

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

$\therefore$ present age of nikhil =

$\pink{ x=8~years.  }$ 

present age of nikita=

$\pink{3x=3×8=24~years.   }$