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In a group of three numbers first is double of second and half of third. The average of three numbers is 56. Find the difference between the first number and third number?
- a)34
- b)48
- c)26
- d)38
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a group of three numbers first is double of second and half of thir...
GIVEN:
First number = 2 × Second Number
First Number = 1/2 × Third number
Average of three numbers = 56
FORMULA USED:
Average = First number + Second number + Third number / 3
CALCULATION:
Let the first number be ‘x’
Second number = x/2
Third number = 2x
According to the question,
(x + x/2 + 2x)/3 = 56
(2x + x + 4x)/6 = 56
7x = 56 × 6
x = 48
∴ Required difference = 96 - 48 = 48
Most Upvoted Answer
In a group of three numbers first is double of second and half of thir...
To solve this problem, let's assume the three numbers as follows:
First number = x
Second number = y
Third number = z
According to the given conditions:
- The first number is double the second number: x = 2y
- The first number is also half the third number: x = z/2
- The average of the three numbers is 56: (x + y + z)/3 = 56
Now, let's solve these equations step by step to find the values of x, y, and z.
Solving for x in terms of y using the equation x = 2y:
- Substitute the value of x in the third equation: 2y = z/2
- Multiply both sides of the equation by 2 to eliminate the fraction: 4y = z
Substituting the value of x in the second equation:
- Substitute the value of x in the second equation: 2y = z/2
- Multiply both sides of the equation by 2 to eliminate the fraction: 4y = z
Now, let's substitute these values in the average equation:
- Substitute the value of x = 2y and z = 4y in the average equation: (2y + y + 4y)/3 = 56
- Simplify the equation: (7y)/3 = 56
- Multiply both sides of the equation by 3 to isolate y: 7y = 168
- Divide both sides of the equation by 7 to solve for y: y = 24
Now that we have the value of y, we can substitute it back into the equations to find the values of x and z.
Substituting y = 24 in the equation x = 2y:
- x = 2(24)
- x = 48
Substituting y = 24 in the equation z = 4y:
- z = 4(24)
- z = 96
Therefore, the first number is 48 and the third number is 96. The difference between the first number and the third number is 96 - 48 = 48.
Hence, the correct answer is option B) 48.
First number = x
Second number = y
Third number = z
According to the given conditions:
- The first number is double the second number: x = 2y
- The first number is also half the third number: x = z/2
- The average of the three numbers is 56: (x + y + z)/3 = 56
Now, let's solve these equations step by step to find the values of x, y, and z.
Solving for x in terms of y using the equation x = 2y:
- Substitute the value of x in the third equation: 2y = z/2
- Multiply both sides of the equation by 2 to eliminate the fraction: 4y = z
Substituting the value of x in the second equation:
- Substitute the value of x in the second equation: 2y = z/2
- Multiply both sides of the equation by 2 to eliminate the fraction: 4y = z
Now, let's substitute these values in the average equation:
- Substitute the value of x = 2y and z = 4y in the average equation: (2y + y + 4y)/3 = 56
- Simplify the equation: (7y)/3 = 56
- Multiply both sides of the equation by 3 to isolate y: 7y = 168
- Divide both sides of the equation by 7 to solve for y: y = 24
Now that we have the value of y, we can substitute it back into the equations to find the values of x and z.
Substituting y = 24 in the equation x = 2y:
- x = 2(24)
- x = 48
Substituting y = 24 in the equation z = 4y:
- z = 4(24)
- z = 96
Therefore, the first number is 48 and the third number is 96. The difference between the first number and the third number is 96 - 48 = 48.
Hence, the correct answer is option B) 48.
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In a group of three numbers first is double of second and half of third. The average of three numbers is 56. Find the difference between the first number and third number?a)34b)48c)26d)38Correct answer is option 'B'. Can you explain this answer?
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