Question

In a series against Australia, the Indian team won six more than half of the matches that Australia won.
A. 4 matches
B. 6 matches
C. 8 matches
D. 10 matches
E. None of these

Answer 1

Hint: In this question, we have to choose the number of matches that were won by Australia. First, we need to take a random variable for the number of matches won by India and then put the variable in the given information we can form a linear equation, by solving the equation we can find out the required solution.

Complete step by step answer:
It is given that, in a series against Australia, the Indian team won six more than half of the matches that Australia won.
Also given that, a total of 12 matches are played.
We have to find out the number of matches Australia won.
Let us consider that the Indian team has won ‘x’ matches.
Since the total number of matches is 12, then Australia must have won $\left( {12 - x} \right)$ matches.
As the Indian team won six more than half of the matches that Australia won thus we get,
$ \Rightarrow x = 6 + \dfrac{1}{2}\left( {12 - x} \right)$
Let us multiply by 2 on both sides we get,
$ \Rightarrow 2x = 12 + 12 - x$
Rearranging the variable and solving the above equation we get,
$ \Rightarrow 3x = 24$
Let us now divide the equation by 3 we get,
$ \Rightarrow x = 8$
Since the India team has won 8 matches, therefore Australia team has won,
$ \Rightarrow 12 - 8 = 4$
Thus, we have found that Australia has won 4 matches.

Hence, option (A) is the correct answer.

Note: Here the linear equation formed with the help of the given particulars it is given that the Indian team won six more than half of the matches that Australia won. This implies that India has won more than 6 games. Since the total number of matches played is 12 we can come to the idea that Australia has won less than 6 games. Which will help clear the three options given.