Question

Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each score?

Answer 1

Hint: Assume the score of Rahul as $ x $ runs. The score of Sachin was $ 2x $ runs. We know that their total runs are $ 198 $ . So, the sum of $ x $ runs and $ 2x $ runs is $ 198 $ . From the linear equation we can find the score of Rahul and Sachin's score is twice the score of Rahul.

Complete step-by-step answer:
It is given that the Sachin score is twice the score of Rahul.
The sum of Rahul score and Sachin score is equal to two less than twice the century.
Let us assume that the score of Rahul is $ x $ runs.
Given that Sachin scores twice as many runs as Rahul.
So the runs scored by Sachin is $ 2x $ .
Also, we know that their total runs fell two short of double the century. So,
 $ x + 2x = 200 - 2 $
We can add the element with the variable terms, that is,
 $ x + 2x = 3x $
Hence, we can say that
  $ 3x = 198 $
On multiplying and dividing both sides by $ 3 $ we get,
 $ \begin{array}{c}
\dfrac{{3x}}{3} = \dfrac{{198}}{3}\\
x = 66
\end{array} $
The runs scored by Rahul is $ 66 $ . The runs scored by Sachin is equal to twice the runs scored by Rahul. So, the runs scored by Sachin is equal to,
 $ 2 \times 66 = 132 $
Hence, the runs scored by Sachin is $ 132 $ .

Note: In linear equations variable terms should be added or subtracted to the same variable term only and constants should be added or subtracted only with constants. For example $ x + 3 = 2x + 2 $ , here we cannot add $ x $ and $ 3 $ or $ 2x $ and $ 2 $ we need to take the common terms same side and then add or subtract that is $ x - 2x = 2 - 3 $ which is $ - x = - 1 $ so $ x = 1 $ .