Question

In a series against Australia, Indian team won six more than half of the matches that Australia won.\[12\] Matches are played, then 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, Indian team won six more than half of the matches that Australia won.
 Also given that, total \[12\] 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 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,
$\Rightarrow$\[x = 8\]
Hence the India team has won \[8\] matches, therefore Australia won \[12 - 8 = 4\] matches.
Hence we have found that Australia has won 4 matches.

Therefore (A) is the correct option.

Additional Information: The linear equations in one variable is an equation which is expressed in the form of \[ax + b = 0\] , where a and b are two integers and x is a variable and has only one solution. For example,\[2x + 8 = 4\] is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is \[2x = 4 - 8 = - 4\]
i.e.\[x = \dfrac{{ - 4}}{2} = - 2\] .

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