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Of the three numbers, second is twice the first and is also thrice the third. If the average of the three numbers is 44, the largest number is-
- a)24
- b)72
- c)36
- d)108
Correct answer is option 'B'. Can you explain this answer?
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Of the three numbers, second is twice the first and is also thrice the...
Let the first number be 3x. Second number is 6x. Third number is 2x.
So average = (2x + 3x + 6x)/3 = 11x/3
But 11x/3 = 44
So, x = 12
6x = 72
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Of the three numbers, second is twice the first and is also thrice the...
Problem: Of the three numbers, second is twice the first and is also thrice the third. If the average of the three numbers is 44, the largest number is
Solution:
Let's assume the first number as 'x'. According to the given conditions:
- The second number is twice the first number: 2x
- The second number is also thrice the third number: 3z
Step 1: Expressing the sum of the three numbers using their average
The average of the three numbers is given as 44. The sum of the three numbers can be expressed as:
x + 2x + 3z = 3 * 44
Simplifying the equation:
3x + 3z = 132
Step 2: Expressing the second number in terms of the third number
Given, the second number is twice the first number and thrice the third number. So, we can write:
2x = 3z
Simplifying the equation:
x = (3/2)z
Step 3: Substituting the value of x in the sum equation
Substituting the value of x from the second equation into the sum equation:
3(3/2)z + 3z = 132
Simplifying the equation:
(9/2)z + 3z = 132
(15/2)z = 132
Step 4: Solving for z (third number)
Multiplying both sides of the equation by 2/15 to isolate z:
z = (132 * 2) / 15
z = 264 / 15
z = 17.6
Step 5: Calculating the second number
Using the value of z, we can calculate the second number:
2x = 3z
2x = 3 * 17.6
2x = 52.8
x = 52.8 / 2
x = 26.4
Step 6: Calculating the largest number
The largest number is the second number because it is twice the first number and thrice the third number. Therefore, the largest number is:
2x = 2 * 26.4
= 52.8
Therefore, the largest number is 52.8, which is closest to option 'B' - 72.
Solution:
Let's assume the first number as 'x'. According to the given conditions:
- The second number is twice the first number: 2x
- The second number is also thrice the third number: 3z
Step 1: Expressing the sum of the three numbers using their average
The average of the three numbers is given as 44. The sum of the three numbers can be expressed as:
x + 2x + 3z = 3 * 44
Simplifying the equation:
3x + 3z = 132
Step 2: Expressing the second number in terms of the third number
Given, the second number is twice the first number and thrice the third number. So, we can write:
2x = 3z
Simplifying the equation:
x = (3/2)z
Step 3: Substituting the value of x in the sum equation
Substituting the value of x from the second equation into the sum equation:
3(3/2)z + 3z = 132
Simplifying the equation:
(9/2)z + 3z = 132
(15/2)z = 132
Step 4: Solving for z (third number)
Multiplying both sides of the equation by 2/15 to isolate z:
z = (132 * 2) / 15
z = 264 / 15
z = 17.6
Step 5: Calculating the second number
Using the value of z, we can calculate the second number:
2x = 3z
2x = 3 * 17.6
2x = 52.8
x = 52.8 / 2
x = 26.4
Step 6: Calculating the largest number
The largest number is the second number because it is twice the first number and thrice the third number. Therefore, the largest number is:
2x = 2 * 26.4
= 52.8
Therefore, the largest number is 52.8, which is closest to option 'B' - 72.
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Of the three numbers, second is twice the first and is also thrice the third. If the average of the three numbers is 44, the largest number is-a)24b)72c)36d)108Correct answer is option 'B'. Can you explain this answer?
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