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

Entered answer:

✅ Correct Answer: 10

We have a football player who has already played some matches (let's call this n), will play 10 more matches, and has scored some goals already (let's call this x).

The key insight is that average = total goals ÷ total matches.

In the first scenario, if he scores 1 goal in the next 10 matches:

Total matches = n + 10

Total goals = x + 1

Average = 0.15 goals per match

Using the average formula:

$\frac{x + 1}{n + 10} = 0.15$

$x + 1 = 0.15(n + 10)$

$x + 1 = 0.15n + 1.5$

$x = 0.15n + 0.5$ ... (Equation 1)

In the second scenario, if he scores 2 goals in the next 10 matches:

Total matches = n + 10

Total goals = x + 2

Average = 0.2 goals per match

$\frac{x + 2}{n + 10} = 0.2$

$x + 2 = 0.2(n + 10)$

$x + 2 = 0.2n + 2$

$x = 0.2n$ ... (Equation 2)

Since both expressions equal x, we can set them equal:

$0.15n + 0.5 = 0.2n$

$0.5 = 0.2n - 0.15n$

$0.5 = 0.05n$

$n = \frac{0.5}{0.05} = \frac{50}{5} = 10$

Pro tip: When dividing by decimals, we multiply both numerator and denominator by 100 to work with whole numbers.

The number of matches he has played is 10.

Key takeaway: When dealing with average problems, we always remember that changing the total by the same amount but adding different quantities will create a system of equations that can be solved efficiently.

2025 Slot 3

The average salary of 5 managers and 25 engineers in a company is 60000 rupees. If each of the managers received 20% salary increase while the salary of the engineers remained unchanged, the average salary of all 30 employees would have increased by 5%. The average salary, in rupees, of the engineers is

CAT 2017 Slot 1

A class consists of $20$ boys and $30$ girls. In the mid-semester examination, the average score of the girls was $5$ higher than that of the boys. In the final exam, however, the average score of the girls dropped by $3$ while the average score of the entire class increased by $2$ . The increase in the average score of the boys is

2025 Slot 2

The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes 66. The number of copies sold on the first day of the book launch is

CAT 2022 Slot 2

Manu earns Rs. $4000$ per month and wants to save an average of Rs. $550$ per month in a year. In the first nine months, his monthly expense was Rs. $3500$ , and he foresees that, tenth month onward, his monthly expense will increase to Rs. $3700$ . In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be

CAT 2023 Slot 3

There are three persons $\mathrm{A}, \mathrm{B}$ and $C$ in a room. If a person $D$ joins the room, the average weight of the persons in the room reduces by $x$ kg . Instead of $D$ , if person $E$ joins the room, the average weight of the persons in the room increases by $2 \mathrm{x} \mathrm{kg}$ . If the weight of $E$ is $12 \mathrm{~kg}$ more than that of $D$ , then the value of $x$ is

CAT 2020 Slot 1

The mean of all $4-$ digit even natural numbers of the form $'aabb',$ where $a > 0,$ is

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)