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Of the four numbers, the first is twice the second, the second is one-third of the third and the third is 5 times the fourth. The average of the numbers is 24.75.The largest of these numbers is:
- a)45
- b)25
- c)30
- d)None of these
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Of the four numbers, the first is twice the second, the second is one-...
Answer – A (45) Explanation – Let the fourth number be a then hen, third number = 5a, second number= 5a/3 and first=10a/3 a+ 5a+ 5a/3 + 10/3 = 24.75 x 4 so,a=9 So, the numbers are 9, 45, 15 and 30
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Of the four numbers, the first is twice the second, the second is one-...
Given Information:
- The first number is twice the second number.
- The second number is one-third of the third number.
- The third number is 5 times the fourth number.
- The average of the four numbers is 24.75.
Let's assign variables to the numbers:
- Let the second number be x.
- The first number is twice the second number, so it is 2x.
- The second number is one-third of the third number, so the third number is 3x.
- The third number is 5 times the fourth number, so the fourth number is 3x/5.
Average of the four numbers:
To find the average of the four numbers, we add them up and divide by 4:
(2x + x + 3x + 3x/5) / 4 = 24.75
Simplifying the equation:
Multiply both sides of the equation by 4 to get rid of the denominator:
2x + x + 3x + 3x/5 = 99
Combining like terms:
Multiplying by 5 to eliminate the fraction:
10x + 5x + 15x + 3x = 495
33x = 495
Solving for x:
Divide both sides of the equation by 33:
x = 15
Finding the largest number:
The largest number is either the first, second, third, or fourth number. Since the first number is twice the second number, it is greater than the second number. The third number is 5 times the fourth number, so it is also greater than the fourth number.
Therefore, the largest number is the third number, which is 3x = 3(15) = 45.
Hence, the correct answer is option A) 45.
- The first number is twice the second number.
- The second number is one-third of the third number.
- The third number is 5 times the fourth number.
- The average of the four numbers is 24.75.
Let's assign variables to the numbers:
- Let the second number be x.
- The first number is twice the second number, so it is 2x.
- The second number is one-third of the third number, so the third number is 3x.
- The third number is 5 times the fourth number, so the fourth number is 3x/5.
Average of the four numbers:
To find the average of the four numbers, we add them up and divide by 4:
(2x + x + 3x + 3x/5) / 4 = 24.75
Simplifying the equation:
Multiply both sides of the equation by 4 to get rid of the denominator:
2x + x + 3x + 3x/5 = 99
Combining like terms:
Multiplying by 5 to eliminate the fraction:
10x + 5x + 15x + 3x = 495
33x = 495
Solving for x:
Divide both sides of the equation by 33:
x = 15
Finding the largest number:
The largest number is either the first, second, third, or fourth number. Since the first number is twice the second number, it is greater than the second number. The third number is 5 times the fourth number, so it is also greater than the fourth number.
Therefore, the largest number is the third number, which is 3x = 3(15) = 45.
Hence, the correct answer is option A) 45.
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