Question

In 2003, Indian cricket team played 60 games and won 30% of the games played. After a phenomenal winning streak, the team raised its average to 50%. How many games did the team win in a row to attain this average?
A. 36
B. 24
C. 48
D. 12

Answer 1

Hint: To solve the question given above, we will first find out how many games Indian cricket team won out of 60 games. After finding this, we will assume that the number of games Indian cricket team played after 60 games is x. Then, we will find the value of x by dividing the total games won by the total games played and multiplying it by 100 and equating it to 50.

Complete step-by-step answer:
It is given in the question that, Indian cricket team played 60 games and won 30% of them. Thus, the total games won by Indian cricket team\[ = {\text{3}}0\% {\text{ of 6}}0\].
Thus, total wins after 60 games = 30% of 60.
Total wins after 60 games \[ = \dfrac{{30}}{{100}} \times 60\]
Total wins after 60 games \[ = \dfrac{{1800}}{{100}}\]
Total wins after 60 games \[ = {\text{18}}\]

Now, it is given in the question that the team played some number of games and won all of them. Due to this their average of winning increased from 30% to 50%. Let the number of games the team played after 60 games be x. Thus the total games played by the team\[ = {\text{6}}0 + {\text{x}}\]. The total games won by the team \[ = 1{\text{8}} + {\text{x}}\] (as they won all of them). Now the winning average after the winning streak is 50%. The winning streak is given by:
\[\begin{array}{l}{\text{Winning streak}} = \dfrac{{{\text{Total wins}}}}{{{\text{Total games played}}}} \times 100\\50 = \dfrac{{18 + x}}{{60 + x}} \times 100\end{array}\]
Now, we will divide the above equation with 100. Then we will get:
\[\begin{array}{l}\dfrac{{50}}{{100}} = \dfrac{{18 + x}}{{60 + x}} \times \dfrac{{100}}{{100}}\\\dfrac{1}{2} = \dfrac{{18 + x}}{{60 + x}}\end{array}\]
Now, we will cross multiply the terms in the equation above. Thus, we will get:
\[\begin{array}{l}60 + x = 2\left( {18 + x} \right)\\60 + x = 36 + 2x\\60 - 36 = 2x - x\\ \Rightarrow x = 24\end{array}\]
Hence, option (b) is correct.

Note: The above question can also be solved alternatively by the following method:
The games won before streak \[ = {\text{y}}\]and the games won after winning streak\[ = {\text{6}}\]. It is given that 50% of total games are won. So, we have
\[50\% {\text{ of }}\left( {x + 60} \right) = x + y\]
\[ \Rightarrow \dfrac{{50}}{{100}} \times \left( {x + 60} \right) = x + y\]. . . . . . . . . . . . . . . . . . . . (i)
\[30\% {\text{ of 60 = y}}\]

\[ \Rightarrow \dfrac{{30}}{{100}} \times 60 = y\]. . . . . . . . . . . . . . . . . . . . . . . . . . . (ii)
We will subtract (ii) from (i). Thus, we will get:
\[\begin{array}{l} \Rightarrow \dfrac{{50}}{{100}}\left( {x + 60} \right) - \dfrac{{30}}{{100}} \times 60 = x + y - y\\ \Rightarrow \dfrac{{x + 60}}{2} - 18 = x\\ \Rightarrow \dfrac{{x + 60 - 36}}{2} = x\\ \Rightarrow x + 24 = 2x\\ \Rightarrow x = 24\end{array}\]