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A bike travels from town P to town $Q$ at an average speed of $50\mathrm{km}/\mathrm{hr}$ and returns from town Q to town P at an average speed of $30\mathrm{km}/\mathrm{hr}$. What is the average speed for the entire trip ?

A school had 105 students with an average age of 30 years. Later, a new batch of students joined. After their inclusion, the average age dropped to 29.5 years, even though the newcomers had an average age of 28 years. Find the number of students in the new batch.

The average age of 12 players of a cricket team is the same as it was 3 years ago because 4 players, whose current average age is 30 years, have been replaced by 4 new players. What is the average age of new players ?

The average of 9 numbers is 57. If the average of the first 4 numbers is 54 and the average of the last 4 numbers is 60 , what is the fifth number?

There are 11 numbers. The average of all 11 is 50 . The average of the first 6 numbers is 48 . The average of the last 6 numbers is 55 . What is the 6th number?

The average age of 22 students is 16 years. If the teacher's age is included, the average rises by 2 year. Later, another teacher joins, and the average rises by 3 more years. What is the age of the second teacher?

The average of four numbers is 30 . The average of the first and second is 25 , and that of the third and fourth is 35 . What is the second number if the first is 20?

At an organization, 4 events were organized. The average attendance for the first two events was 168.5 people. The next two events had an average of 182.5 people. Later, due to a correction, it was found that the attendance at one of the first two events was 15 more than what was originally recorded, and one of the last two events was 7 less. Find the corrected overall average attendance for all 4 events.

Which of the following statements is/are INCORRECT ? I. The average of 8 numbers is 25 . If one number is removed, the average of the remaining 7 numbers becomes 24 , then the removed number is 32 . II. If instead, the removed number was 18 , the average of the remaining 7 numbers would be 26 .

The average age of 25 students is 16 years. A group of 5 new students joins, increasing the average to 18 years. Find the average age of the 5 new students.

The average monthly salary of employees in a company is ₹ 60,000 . When 6 new employees with average salary ₹45,000 join, the average salary of the whole company decreases by ₹6,000. Find the original number of employees.

A group of 8 students appeared for a chemistry test. The average of the top 4 scores was 88.5 , and the average of the bottom 4 scores was 74. Later, it was found that a decimal error had occurred, and one of the scores from the bottom half was recorded as 71.2 instead of 91.2. What is the corrected overall average of the group?

The average marks of 10 students in a mathematics test are 73.5. Later, it was found that one student's score was misread as 45 instead of 54. After correcting this error, another student's marks were removed for being invalid, and the average of the remaining 9 students rose to 76.2 . Find the marks of the student whose score was removed.

A factory hired 10 workers and found that their average productivity per day was 43.75 unit. Later, 3 more workers were hired. The average productivity of all 13 workers then became 46.5 units. However, one of the new 3 workers made 50.2 unit daily, and another made 46.4 unit daily. What is the daily productivity of the third new worker?

The average of 15 numbers is 30 . If 5 is added to 40% of the numbers and 3 is subtracted from the remaining 60% of the numbers, what will be the new average?

The average of 7 consecutive odd natural numbers is 39. Previous 7 consecutive odd natural numbers to these 7 odd natural numbers are also included. What will be the average of newly added numbers ?

The average of 5 consecutive odd natural numbers is 57. Previous 5 consecutive odd natural numbers to these 5 odd natural numbers are also included. What will be the average of newly added numbers?

In a science club, the average score of 20 students in a monthly test is 68.5. After including the scores of 4 more students, the overall average becomes 70.2 . If the scores of two of the new students are 72.5 and 75.5 , respectively, and the remaining two students have equal scores, find the score of each of the remaining two students.