Question

Five years ago, Shikha was thrice as old as Rani. 10 years later, Sikha will be twice as old as Rani. How old are they now?
$
  (a){\text{ shikha 50, rani 20}} \\
  (b){\text{ shikha 20, rani50}} \\
  (c){\text{ shikha 30, rani 80}} \\
  (d){\text{ none}} \\
 $

Answer 1

Hint – In this question let the present age of Shikha be x years and the present age of Rani be y years. Then use the constraints of the questions to formulate two linear equations involving two variables. Solve them to get the right option.
Complete step-by-step answer:
Let the present age of the Shikha be x years.
And the present age of his Rani is y years.
Now it is given that five years ago, Shikha was thrice as old as Rani.
Now construct the linear equation according to given information we have,
Age of Shikha five years ago is equal to 3 multiplied by the age of Rani five years ago.
$ \Rightarrow x - 5 = 3\left( {y - 5} \right)$…………………….. (1)
Now it is also given that after 10 years Shikha will be twice as old as Rani.
Now again construct the linear equation according to given information we have,
$ \Rightarrow \left( {x + 10} \right) = 2\left( {y + 10} \right)$…………………….. (2)
Now from equation (1) the value of x is
$ \Rightarrow x = 3\left( {y - 5} \right) + 5 = 3y - 10$
Now put the value of x from equation (1) in equation (2) we have,
$ \Rightarrow \left( {3y - 10 + 10} \right) = 2\left( {y + 10} \right)$
Now simplify the above equation we have,
$ \Rightarrow 3y = 2y + 20$
$ \Rightarrow y = 20$Years.
Now put the value of y in equation (1) we have,
$ \Rightarrow x - 5 = 3\left( {20 - 5} \right) = 45$
Now simplify the above equation we have,
$ \Rightarrow x = 45 + 5 = 50$ Years.
So, the present age of the Shikha is 50 years and the present age of Rani is 20 years.
So, this is the required answer.
Hence option (A) is correct.

Note – Whenever we have to solve two linear equations involving two variables there can be two ways to do it, above we have used the first method of substitution, another method is by elimination. In this method we make the coefficients of any one variable present in both the equations as same and then eliminate this variable by specific operation of addition/subtraction.