Practice Questions
The average of 12 numbers is 35. If two numbers 40 and 50 are replaced by 30 and 60, find the new average.
Sum of replaced numbers ($40+50=90$) is equal to the sum of new numbers ($30+60=90$). Since the total sum remains unchanged, the average remains 35.
The average weight of 15 students is 50 kg. If one student weighing 60 kg leaves and another joins, the average becomes 49 kg. Find the weight of the new student.
Total weight decrease = $15 \times (50 - 49) = 15$ kg. Weight of new student = $60 - 15 = 45$ kg.
The average of first n natural numbers is 20. Find n.
Average = $(n+1)/2 = 20 \Rightarrow n+1 = 40 \Rightarrow n = 39$.
The average marks of a class increased from 60 to 63 when 5 new students joined. Find the average marks of the new students if original strength was 25.
Original total = $25 \times 60 = 1500$. New total = $30 \times 63 = 1890$. Sum of 5 new students = 390. Average = $390/5 = 78$.
A batsman has an average of 48 runs in 20 innings. How many runs must he score in the next 5 innings to raise the average to 52?
Total runs needed for 25 innings = $25 \times 52 = 1300$. Current runs = $20 \times 48 = 960$. Runs needed = $1300 - 960 = 340$.
The average age of a group increases by 2 years when a person aged 24 replaces a person aged 18. Find the number of persons in the group.
Increase in sum = $24 - 18 = 6$. Since average increased by 2, number of persons = $6/2 = 3$.
The average temperature for Monday, Tuesday, and Wednesday is 30°C. The average for Tuesday, Wednesday, and Thursday is 33°C. If Thursday's temperature is 31°C, find Monday's temperature.
$M+T+W = 3 \times 30 = 90$. $T+W+Th = 3 \times 33 = 99$. So $T+W = 99 - 31 = 68$. Then $M = 90 - 68 = 22°C$.
The average score of a cricketer in 10 matches is 38. If the average for the first 6 matches is 42, find the average for the last 4 matches.
Total of 10 matches = $10 \times 38 = 380$. Total of first 6 = $6 \times 42 = 252$. Total of last 4 = $380 - 252 = 128$. Average of last 4 = $128/4 = 32$.
The average of 11 numbers is 50. If the average of the first 5 numbers is 48 and the average of the last 5 numbers is 52, find the 6th number.
Sum of 11 numbers = $11 \times 50 = 550$. Sum of first 5 = $5 \times 48 = 240$. Sum of last 5 = $5 \times 52 = 260$. 6th number = $550 - 240 - 260 = 50$.
The average of 8 numbers is 15. If each number is multiplied by 3, what is the new average?
If each number is multiplied by 3, the sum gets multiplied by 3, so the average also gets multiplied by 3. New average = $15 \times 3 = 45$.
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