Average
- Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, then difference of first and third number is
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Let the numbers be 2k, k and 4k respectively
∴ Average = 2k + k + 4k 3 ⇒ 7k = 56 3 ⇒ k = 3 × 56 = 24 7
∴ First number = 2k = 2 × 24 = 48
Third number = 4k = 4 × 24 = 96
∴ Required difference = Third number - First number = 96 – 48 = 48
Second method to solve this question with the help of given formulas :
Here, a = 2, b = 1/4 , X = 56First number = 3ab × X 1 + b + ab First number = 3 × 2 × 1 × 56 4 1 + 1 + 2 × 1 4 4
Correct Option: D
Let the numbers be 2k, k and 4k respectively
∴ Average = 2k + k + 4k 3 ⇒ 7k = 56 3 ⇒ k = 3 × 56 = 24 7
∴ First number = 2k = 2 × 24 = 48
Third number = 4k = 4 × 24 = 96
∴ Required difference = Third number - First number = 96 – 48 = 48
Second method to solve this question with the help of given formulas :
Here, a = 2, b = 1/4 , X = 56First number = 3ab × X 1 + b + ab First number = 3 × 2 × 1 × 56 4 1 + 1 + 2 × 1 4 4 First number = 3 × 4 × 56 = 48 2 4 + 1 + 2 Third number = 3 × X 1 + b + ab Third number = 3 × 56 1 + 1 + 2 × 1 4 4 Third number = 3 × 4 × 56 = 96 4 + 4 + 2
Required difference = 96–48 = 48
- The average of three numbers is 28, the first number is half of the second, the third number is twice the second, then the third number is
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Let the second number be p.
Then first number = p 2
and third number = 2pAccording to the question, p + p + 2p = 28 × 3 2 ⇒ p + 2p + 4p = 28 × 3 2
⇒ 7p = 28 × 3 × 2⇒ 168 = 24 7
∴ Third number = 2 × 24 = 48
Second method to solve this question with the help of given formulas :
Here, a = 1 , b = 1 , X = 28 2 2 Third number = 3 × X 1 + b + ab
Correct Option: A
Let the second number be p.
Then first number = p 2
and third number = 2pAccording to the question, p + p + 2p = 28 × 3 2 ⇒ p + 2p + 4p = 28 × 3 2
⇒ 7p = 28 × 3 × 2⇒ 168 = 24 7
∴ Third number = 2 × 24 = 48
Second method to solve this question with the help of given formulas :
Here, a = 1 , b = 1 , X = 28 2 2 Third number = 3 × X 1 + b + ab Third number = 3 × 28 1 + 1 + 1 × 1 2 2 2 Third number = 3 × 28 4 + 2 + 1 4 Third number = 3 × 4 × 28 = 48 7
- Mean of 10 numbers is 30. Later on it was observed that numbers 15, 23 are wrongly taken as 51, 32. The correct mean is
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Later on it was observed that numbers 15, 23 are wrongly taken as 51, 32 .
∴ Difference = 15 + 23 – 51 – 32 = –45∴ Correct average = 30 - 45 = 25.5 10
Second method to solve this question with the help of given formula :
Here, n = 10, m = 30 , a = 15, b = 23 , p = 51 , q = 32Correct Average = m + (a + b - p - q) n Correct Average = 30 + (15 + 23 - 51 - 32) 10
Correct Option: A
Later on it was observed that numbers 15, 23 are wrongly taken as 51, 32 .
∴ Difference = 15 + 23 – 51 – 32 = –45∴ Correct average = 30 - 45 = 25.5 10
Second method to solve this question with the help of given formula :
Here, n = 10, m = 30 , a = 15, b = 23 , p = 51 , q = 32Correct Average = m + (a + b - p - q) n Correct Average = 30 + (15 + 23 - 51 - 32) 10 Correct Average = 30 + 
38 - 83 
10 Correct Average = 30 - 45 = 25.5 10
Correct Average = 30 – 4.5 = 25.5
- A tabulator while calculating the average marks of 100 students of an examination, by mistake enters 68, instead of 86 and obtained the average as 58; the actual average marks of those students is
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On the basis of given details in question , we have
Difference = 86 – 68 = 18∴ Actual average = 58 + 18 100
Actual average = 58.18
Second method to solve this question with the help of given formula :
Here, n = 100 , m = 58 , a = 86 , b = 68Correct Average = m + (a - b) n
Correct Option: A
On the basis of given details in question , we have
Difference = 86 – 68 = 18∴ Actual average = 58 + 18 100
Actual average = 58.18
Second method to solve this question with the help of given formula :
Here, n = 100 , m = 58 , a = 86 , b = 68Correct Average = m + (a - b) n Correct Average = 58 + (86 - 68) 100
Correct Average = 58 + 18 100
Correct Average = 58 + 0.18 = 58.18
- The mean of 20 items is 47. Later it is found that the item 62 is wrongly written as 26. Find the correct mean.
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Later it is found that the item 62 is wrongly written as 26 ,
∴ Difference = 62 – 26 = 36∴ Required average = 47 + 36 20
Required average = 47 + 1.8 = 48.8
Second method to solve this question with the help of given formula :
Here, n = 20 , m = 47 , a = 62 , b = 26Correct Average = m + (a - b) n
Correct Option: A
Later it is found that the item 62 is wrongly written as 26 ,
∴ Difference = 62 – 26 = 36∴ Required average = 47 + 36 20
Required average = 47 + 1.8 = 48.8
Second method to solve this question with the help of given formula :
Here, n = 20 , m = 47 , a = 62 , b = 26Correct Average = m + (a - b) n Correct Average = 47 + (62 - 26) 20 Correct Average = 47 + 36 20
Correct Average = 47 + 1.8 = 48.8
