Average
Finding the missing numbers when average of numbers is given
Question (1) The average weight of John, Rosy, and Sujuka is 45 kg. If the average weight of John and Rosy is 30 kg and that of Rosy and Sujuka is 45 kg, then find the weight of Rosy.
Solution
Given, Average weight of John, Rosy, and Sujuka = 45
Thus, their total weight = 3 × 45
= 135 kg
Again, given the average weight of John and Rosy = 30 kg
Thus, their total weight = 2 × 30
= 60 kg
Again, given, the average weight of Rosy and Sujuka = 45 kg
Thus, their total weight = 2 × 45 = 90 kg
Now, the weight of Rosy = (Total weight of John and Rosy + Total weight of Rosy and Sujaka) – Total weight of John, Rosy, and Sujaka
= (60 kg + 90 kg) – 135 kg
= 150 kg – 135 kg
= 15 kg
Thus, weight of Rosy = 15 kg Answer
Shortcut Method to solve the given question based on average
Let the weight of John = J, weight of Rosy = R and weight of Sujuka = S
Now, given, average weight of J, R and S = 45 kg
Thus, J + R + S = 3 × 45 kg = 135
And, average weight of J and R = 30 kg
Thus, J + R = 2 × 30 = 60 kg
And, average weight of R and S = 30 kg
Thus, R + S = 2 × 30 kg
Thus, weight of Rosy (R) = ?
The weight of Rosy = (J + R) + ( R + S) – (J + R + S)
= J + R + R + S – R – S
= R
Thus, weight of Rosy (R) = (J + R) + ( R + S) – (J + R + S)
= 60 kg + 90 kg – 135 kg
= 150 kg – 135 kg
⇒ R = 15 kg
Thus, weight of Rosy = 15 kg Answer
Question (2) 15 chairs are bought at the rate of Rs 400 per chair. 5 chairs are bought at the rate of Rs 900 per chair. If 20 more chairs are bought at the rate of Rs 700 per chair, then what is the average price of the chair?
Solution
Given, that 15 chairs are bought at the rate of Rs 400 per chair.
Thus, total price of 15 chairs = 15 × Rs 400
= Rs 6000.00
Again, given 5 chairs are bought at the rate of Rs 900 per chair.
Thus, total price of 5 chairs = 5 × Rs 900
= Rs 4500
Again, given, 20 more chairs are bought at the rate of Rs 700 per chair.
Thus, total price of 20 chairs = 20 × Rs 700
= Rs 14000
Thus, the total price of all the chairs = Price of 15 chairs + Price of 5 chairs + Price of 20 chairs
= 6000 + 4500 + 14000
= Rs 24500.00
Now, total number of chairs = 15 + 5 + 20 = 40
Thus, total number of chairs = 40
Thus, the average price of chairs = Total price of chairs/Number of chairs
`=24500/40 = Rs 612.50`
Thus, average price per chair = Rs 612.50 Answer
Question (3) 20 chairs are bought at the rate of $ 10 per chair. 15 chairs are bought at the rate of $12 per chair. If 150 more chairs are bought at the rate of $ 21 per chair, then find the average price of chairs.
Solution
Given, that 20 chairs are bought at the rate of $10 per chair.
Thus, total price of 20 chairs = 20 × $10
= $ 200.00
Again, given 15 chairs are bought at the rate of $12 per chair.
Thus, total price of 15 chairs = 15 × $12
= $180.00
Again, given, 50 more chairs are bought at the rate of $21 per chair.
Thus, total price of 50 chairs = 50 × $21
= $ 1050.00
Thus, the total price of all the chairs = Price of 20 chairs + Price of 15 chairs + Price of 50 chairs
= $200 + $180 + $ 1050
= $1430.00
Now, total number of chairs = 20+ 15 + 50 = 85
Thus, total number of chairs = 85
Thus, the average price of chairs = Total price of chairs/Number of chairs
`=1450/85 = $16.82`
Thus, average price per chair = $16.82 Answer
Question (4) If the average of 5, 8, 10, 12 and m is 12 then find the value of m.
Solution
Given, the average of 5, 8, 10, 12 and m = 12
Then, value of m = ?
Here numbers of given all digits = 5
Thus, Average = Sum of all numbers/total number of numbers
After cross multiplication, we get
12 × 5 = 35 + m
⇒ 60 = 35 + m
⇒ 35 + m = 60
⇒ m = 60 – 35
⇒ m = 25 Answer
Question (5) The average of 12, 6, 10, 25, 7 and y is 15. What is the value of y?
Solution
Given, the average of 12, 6, 10, 25, 7 and y = 15
Then, value of y = ?
Here numbers of given all digits = 6
Thus, Average = Sum of all numbers/total number of numbers
After cross multiplication, we get
15 × 6 = 53 + y
⇒ 90 = 53 + y
⇒ 53 + y = 90
⇒ y = 90 – 53
⇒ y = 37 Answer
Question (6) The average of 5, 2, 7, and m is 10, and the average of 6, 8, 9 ,2, m and n is 12, then find the values of m and n.
Solution
Given, average of 5, 2, 7, and m = 10
And, average of 6, 8, 9 ,2, m and n = 12
Then values of m and n = ?
We know that, Average = Sum of all numbers/total number of numbers
After cross multiplication
⇒ 10 × 4 = 14 + m
⇒ 40 = 14 + m
After rearrangement of above expressions
⇒ 14 + m = 40
⇒ m = 40 – 14
⇒ m = 26 - - - - (i)
Now, for the second condition,
Average = Sum of all numbers/total number of numbers
After cross multiplication
⇒ 12 × 6 = 25 + m + n
After substituting the value of m from equation (i) in the above expression, we get
72 = 25 + 26 + n
⇒ 72 = 51 + n
⇒ 72 – 51 = n
⇒ 21 = n
⇒ n = 21
Thus, value of m = 26 and n = 21 Answer
Question (7) The average of 3, 5, 11, and m is 10, and the average of 7, 9, 11, 5, m, and n is 12, then find the values of m and n.
Solution
Given, average of 3, 5, 11, and m = 10
And, average of 7, 9, 11, 5, m and n = 12
Then values of m and n = ?
We know that, Average = Sum of all numbers/total number of numbers
After cross multiplication
⇒ 10 × 4 = 18 + m
⇒ 40 = 18 + m
After rearrangement of above expressions
⇒ 18 + m = 40
⇒ m = 40 – 18
⇒ m = 22 - - - - (i)
Now, for the second condition,
Average = Sum of all numbers/total number of numbers
After cross multiplication
⇒ 12 × 6 = 32 + m + n
After substituting the value of m from equation (i) in the above expression, we get
72 = 32 + 22 + n
⇒ 72 = 54 + n
⇒ 72 – 54 = n
⇒ 18 = n
⇒ n = 18
Thus, value of m = 22 and n = 18 Answer
Question (8) The average of 14, 12, and m is 16, and the average of 22, 8, 7, m, and n is 25, then find the values of m and n.
Solution
Given, average of 14, 12, and m = 16
And, average of 22, 8, 7, m and n = 25
Then values of m and n = ?
We know that, Average = Sum of all numbers/total number of numbers
After cross multiplication
⇒ 16 × 3 = 26 + m
⇒ 48 = 26 + m
After rearrangement of above expressions
⇒ 26 + m = 48
⇒ m = 48 – 26
⇒ m = 22 - - - - (i)
Now, for the second condition,
Average = Sum of all numbers/total number of numbers
After cross multiplication
⇒ 25 × 5 = 37 + m + n
After substituting the value of m from equation (i) in the above expression, we get
125 = 37 + 22 + n
⇒ 125 = 59 + n
⇒ 125 – 59 = n
⇒ 66 = n
⇒ n = 66
Thus, value of m = 22 and n = 66 Answer
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