Averages , Ratio and Proportion Question 9 - CAT 2021
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:
Step-by-Step Explanation
Let the number of matches played so far be m and the goals scored so far be g.
The total number of matches played by the end of the tournament will be m + 10.
- Set up the linear average systems:
- Case 1 (1 goal over the next 10 matches):
(g + 1)/(m + 10) = 0.15
g + 1 = 0.15(m + 10) --- (Equation 1)
- Case 2 (2 goals over the next 10 matches):
(g + 2)/(m + 10) = 0.20
g + 2 = 0.20(m + 10) --- (Equation 2)
- Solve by subtraction:
Subtract Equation 1 from Equation 2:
(g + 2) − (g + 1) = 0.20(m + 10) − 0.15(m + 10)
1 = 0.05(m + 10)
m + 10 = 1/0.05 = 20
Total matches = 20
m = 20 − 10 = 10 matches played initially
Correct Answer: 10