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The mean of six numbers is 47. If one number is excluded, their mean becomes 41. The excluded number is
- a)77
- b)78
- c)60
- d)45
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The mean of six numbers is 47. If one number is excluded, their mean b...
Concept:
Mean = (Sum of observations) / (Total number of observations)
Mean = (Sum of observations) / (Total number of observations)
Calculation:
Let the six numbers be a, b, c, d, e, f
So, Mean
⇒ a + b + c + d + e + f = 282 ....(1)
Let, the excluded number be a,
So mean of remaining five numbers
⇒ b + c + d + e + f = 205 ....(2)
∴ a + 205 = 282 (from (1) and (2))
⇒ a = 77
Hence, option (1) is correct.
Let the six numbers be a, b, c, d, e, f
So, Mean
⇒ a + b + c + d + e + f = 282 ....(1)
Let, the excluded number be a,
So mean of remaining five numbers
⇒ b + c + d + e + f = 205 ....(2)
∴ a + 205 = 282 (from (1) and (2))
⇒ a = 77
Hence, option (1) is correct.
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Community Answer
The mean of six numbers is 47. If one number is excluded, their mean b...
The mean of six numbers is 47, and if one number is excluded, their mean becomes 41. We need to find the excluded number from the given options.
To solve this problem, we can use the concept of the mean and sum of numbers.
Let's denote the sum of the six numbers as X, and the excluded number as Y.
The mean of the six numbers is 47, which means that the sum of the six numbers divided by 6 is equal to 47:
X/6 = 47
If one number is excluded, the mean becomes 41, which means that the sum of the remaining five numbers divided by 5 is equal to 41:
(X - Y)/5 = 41
Now we have two equations with two variables. We can solve these equations simultaneously to find the values of X and Y.
Solving equation 1 for X:
X = 6 * 47
X = 282
Substituting the value of X in equation 2:
(282 - Y)/5 = 41
Multiplying both sides of the equation by 5:
282 - Y = 205
Subtracting 282 from both sides:
-Y = -77
Multiplying both sides by -1:
Y = 77
Therefore, the excluded number is 77, which corresponds to option A.
To solve this problem, we can use the concept of the mean and sum of numbers.
Let's denote the sum of the six numbers as X, and the excluded number as Y.
The mean of the six numbers is 47, which means that the sum of the six numbers divided by 6 is equal to 47:
X/6 = 47
If one number is excluded, the mean becomes 41, which means that the sum of the remaining five numbers divided by 5 is equal to 41:
(X - Y)/5 = 41
Now we have two equations with two variables. We can solve these equations simultaneously to find the values of X and Y.
Solving equation 1 for X:
X = 6 * 47
X = 282
Substituting the value of X in equation 2:
(282 - Y)/5 = 41
Multiplying both sides of the equation by 5:
282 - Y = 205
Subtracting 282 from both sides:
-Y = -77
Multiplying both sides by -1:
Y = 77
Therefore, the excluded number is 77, which corresponds to option A.
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The mean of six numbers is 47. If one number is excluded, their mean becomes 41. The excluded number isa)77b)78c)60d)45Correct answer is option 'A'. Can you explain this answer?
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