Question:medium

In a football tournament, a player has played a certain number of matches and 10 more matches are to be played. If he scores a total of one goal over the next 10 matches, his overall average will be 0.15 goals per match. On the other hand, if he scores a total of two goals over the next 10 matches, his overall average will be 0.2 goals per match. The number of matches he has played is

Updated On: Jan 15, 2026
Show Solution

Correct Answer: 10

Solution and Explanation

Let \( x \) represent the number of matches previously played.

The player participates in an additional 10 matches. Two scenarios are considered:

  1. Scenario 1: Assuming the player scores 1 goal across these 10 matches, the updated average is calculated as: \[ \text{Average} = 0.15 \]
  2. Scenario 2: If the player scores 2 goals in these 10 matches, the updated average is: \[ \text{Average} = 0.20 \]

Therefore, scoring 1 more goal results in an increase of the average from 0.15 to 0.20, representing a change of:

\[ 0.20 - 0.15 = 0.05 \]

This average increase of 0.05 per goal implies the following relationship:

\[ \frac{1 \text{ goal}}{x + 10 \text{ matches}} = 0.05 \Rightarrow x + 10 = \frac{1}{0.05} = 20 \]

This calculation indicates that the total number of matches played, including the additional 10, is 20.

\[ \Rightarrow x = 20 - 10 = 10 \]

Final Result:

The number of matches previously played is 10

Was this answer helpful?
0

Top Questions on Average

Questions Asked in CAT exam

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
View Solution