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Of the 3 numbers whose average is 26, the first is 2/11 times the sum of other two. The first number is.
- a)16
- b)13
- c)11
- d)12
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Of the 3 numbers whose average is 26, the first is 2/11 times the sum ...
Let the numbers are a, b and c
⇒ a + b + c = 26 × 3 = 78
⇒ a = 2/11 × (b + c)
⇒ a + 11a/2 = 78
⇒ 13a/2 = 78
⇒ a = 12
∴ First number is 12.
⇒ a + b + c = 26 × 3 = 78
⇒ a = 2/11 × (b + c)
⇒ a + 11a/2 = 78
⇒ 13a/2 = 78
⇒ a = 12
∴ First number is 12.
Most Upvoted Answer
Of the 3 numbers whose average is 26, the first is 2/11 times the sum ...
Given information:
- The average of three numbers is 26.
- The first number is 2/11 times the sum of the other two numbers.
Let's assume the three numbers as:
First number = x
Second number = y
Third number = z
Average of the three numbers:
(x + y + z)/3 = 26
First number is 2/11 times the sum of the other two numbers:
x = (2/11)(y + z)
To solve this problem, we can use the given information to form equations and then solve them simultaneously.
Equation 1: Average of the three numbers
(x + y + z)/3 = 26
Equation 2: First number is 2/11 times the sum of the other two numbers
x = (2/11)(y + z)
Solving the equations simultaneously:
Multiply equation 2 by 11 to eliminate the fraction:
11x = 2(y + z)
Now substitute this value of 11x in equation 1:
(11x + y + z)/3 = 26
Simplify equation 1:
11x + y + z = 3 * 26
11x + y + z = 78
Substitute the value of 11x from equation 2:
2(y + z) + y + z = 78
3y + 3z = 78
y + z = 78/3
y + z = 26
Now, we have two equations:
y + z = 26
x = (2/11)(y + z)
Substitute the value of y + z in the second equation:
x = (2/11)(26)
x = 52/11
x = 4.727
Since the numbers given in the options are integers, we need to find the closest integer to 4.727, which is 5.
Therefore, the first number is 5, which matches with option D) 12.
Hence, the correct answer is option D) 12.
- The average of three numbers is 26.
- The first number is 2/11 times the sum of the other two numbers.
Let's assume the three numbers as:
First number = x
Second number = y
Third number = z
Average of the three numbers:
(x + y + z)/3 = 26
First number is 2/11 times the sum of the other two numbers:
x = (2/11)(y + z)
To solve this problem, we can use the given information to form equations and then solve them simultaneously.
Equation 1: Average of the three numbers
(x + y + z)/3 = 26
Equation 2: First number is 2/11 times the sum of the other two numbers
x = (2/11)(y + z)
Solving the equations simultaneously:
Multiply equation 2 by 11 to eliminate the fraction:
11x = 2(y + z)
Now substitute this value of 11x in equation 1:
(11x + y + z)/3 = 26
Simplify equation 1:
11x + y + z = 3 * 26
11x + y + z = 78
Substitute the value of 11x from equation 2:
2(y + z) + y + z = 78
3y + 3z = 78
y + z = 78/3
y + z = 26
Now, we have two equations:
y + z = 26
x = (2/11)(y + z)
Substitute the value of y + z in the second equation:
x = (2/11)(26)
x = 52/11
x = 4.727
Since the numbers given in the options are integers, we need to find the closest integer to 4.727, which is 5.
Therefore, the first number is 5, which matches with option D) 12.
Hence, the correct answer is option D) 12.
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Of the 3 numbers whose average is 26, the first is 2/11 times the sum of other two. The first number is.a)16b)13c)11d)12Correct answer is option 'D'. Can you explain this answer?
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