Question

Five years ago, Shikha was thrice as old as Rani. Ten years later, Shikha will be twice as old as Rani. How old are they now?
A.Rani 20 yrs, Shikha 50 yrs
B.Shikha 20 yrs, Rani 50 yrs
C.Shikha 80 yrs, Rani 30 yrs
D.Shikha 30 yrs, Rani 80 yrs

Answer 1

Hint: First make the equation of the condition by taking the unknown value as variable then solve the equation by taking any method (substitution, elimination or cross multiplication).

Complete step-by-step answer:
Consider, the present age of Shikha is x years and the present age of Rani is y years.
Five year ago,
The age of Shikha is $x - 5$ years.
The age of Rani is $y - 5$ years.
According to the question,
The age of Shikha is thrice of Rani then we get,
$\left( {x - 5} \right) = 3\left( {y - 5} \right)$
Solving this expression we get,
$
\Rightarrow x - 5 = 3y - 15\\
\Rightarrow x - 3y = 5 - 15\\
\Rightarrow x - 3y = - 10\;...........................(i)
$
Ten year later,
The age of Shikha will be $x + 10$ years.
The age of Rani will be $y + 10$ years.
According to the question,
The age of Shikha will be twice of Rani then we get,
$\left( {x + 10} \right) = 2\left( {y + 10} \right)$
Solving this expression we get,
 $
\Rightarrow x + 10 = 2y + 20\\
\Rightarrow x - 2y = - 10 + 20\\
\Rightarrow x - 2y = 10\;...........................(ii)
$
Taking the first equation as:
$
\Rightarrow x - 3y = - 10\\
\Rightarrow x = 3y - 10
$
Substituting the value of x in equation (ii) then we get,
$\left( {3y - 10} \right) - 2y = 10$
Simplifying the equation then,
$
\Rightarrow 3y - 10 - 2y = 10\\
\Rightarrow y = 10 + 10\\
\Rightarrow y = 20
$
Substituting the value of y in equation (i) then we get,
$x - 3y = - 10$
Simplifying the equation then,
$
\Rightarrow x - 3 \times 20 = - 10\\
\Rightarrow x - 60 = - 10\\
\Rightarrow x = 60 - 10\\
\Rightarrow x = 50
$
The present age of Shikha is x as the value of x is 50. So the present age of Shikha is 50 yrs.
Similarly, the present age of Rani is y as the value of y is 20. So the present age of Rani is 20 yrs.
So, the correct answer is “Option A”.

Note: In this type of problem make the equations as per the condition given. Also you can check your answer by placing the value of x and y again in the equation if the values satisfying the equation then answer is correct otherwise it is wrong so you have to check it again.