In a school, Class A has 24 students with an average height of 160 cm, and Class B has 20 students with an average height of 168 cm. The average height of students in Class C is 165 cm. If the overall average height of all students from Classes A, B and C is 164 cm, find the number of students in Class C.
16
Let the number of students in Class C be \(x\).
Total height of Class A \(= 24 \times 160 = 3840\) cm.
Total height of Class B \(= 20 \times 168 = 3360\) cm.
Total height of Class C \(= 165x\) cm.
Total students \(= 44 + x\), and overall average is 164 cm, so:
\(\frac{3840 + 3360 + 165x}{44 + x} = 164\)
\(7200 + 165x = 7216 + 164x\)
\(x = 16\)
Hence, the number of students in Class C is 16.
Similar Questions
- The average of first 167 even numbers is
- The average price of three items of furniture is ₹5,310. If their prices are in the ratio 3 : 5 : 7, the price of the cheapest item (in ₹) is:
- The average price of three items of furniture is ₹5,305. If their prices are in the ratio 3 : 5 : 7, the price of the cheapest item (in ₹) is:
- The average price of three items of furniture is ₹16875. If their prices are in the ratio 3:5:7, the price of the costliest item (in ₹) is
- If the average of $a_1, a_2, a_3$ and $a_4$ is $19.5$, $a_1 = 21$ and the average of $a_1, a_2$ and $a_3$ is equal to the average of $a_2, a_3$ and $a_4$, then what will be the value of $a_4$ ?
- The average runs scored by a batsman in 23 matches is 43. In the next 10 matches, the batsman scored an average of 16 runs. Find his average runs scored (rounded off to two decimal places) in all the 33 matches.
- The arithmetic mean of x observations is m. If two observations 0 and m are added, then the new mean will be:
- The average weight of Mandar, Ketan and Tushar is 45 kg. If the average weight of Mandar and Ketan is 44 kg and that of Ketan and Tushar is 45 kg, then the weight of Ketan (in kg) is:
- The average of first 165 even numbers is
- The average price of three items of furniture is ₹16,005. If their prices are in the ratio 3 : 5 : 7, the price of the cheapest item (in ₹) is:
Important Questions from Average
The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14 th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)
24 students collected money for donation. The average contribution was Rs. 50. Later on, their teacher also contributed some money. Now the average contribution is Rs. 56. The teacher’s contribution is:
Out of 6 numbers, the sum of the first 5 numbers is 7 times the 6 th number. If their average is 136, then the 6 th number is:
The average of five numbers is 30. If one number is excluded, then average becomes 31. What is the excluded number?
The average weight of 49 students in a class is 39 kg. Seven of them whose average weight is 40 kg leave the class and other seven students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?
