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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)15
Correct answer is option 'A'. Can you explain this answer?
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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 assume the second number as 'x'. Based on the given information, we can determine the values of the other three numbers as follows:
- The first number = 2 * x (twice the second number)
- The third number = 3 * x (one-third of the second number)
- The fourth number = x / 5 (one-fifth of the third number)
Now, let's find the average of these four numbers:
Average = (First + Second + Third + Fourth) / 4
24.75 = (2x + x + 3x + x/5) / 4
Simplifying the equation:
24.75 = (11x + x/5) / 4
99 = 55x + x/5
99 = (275x + x) / 5
495 = 276x
x = 495 / 276
x ≈ 1.79
So, the second number is approximately 1.79.
Finding the other numbers:
- The first number = 2 * 1.79 ≈ 3.58
- The third number = 3 * 1.79 ≈ 5.37
- The fourth number = 1.79 / 5 ≈ 0.36
Now, let's check if the average of these numbers is indeed 24.75:
Average = (3.58 + 1.79 + 5.37 + 0.36) / 4
Average ≈ 11.1
Since the calculated average is not equal to 24.75, our assumption for the second number (x) is incorrect.
Let's try a different assumption for the second number.
Let's assume the second number as 'y'. Based on the given information, we can determine the values of the other three numbers as follows:
- The first number = 2 * y (twice the second number)
- The third number = 3 * y (one-third of the second number)
- The fourth number = y / 5 (one-fifth of the third number)
Now, let's find the average of these four numbers:
Average = (First + Second + Third + Fourth) / 4
24.75 = (2y + y + 3y + y/5) / 4
Simplifying the equation:
24.75 = (7y + y/5) / 4
99 = 35y + y/5
99 = (175y + y) / 5
495 = 176y
y = 495 / 176
y ≈ 2.81
So, the second number is approximately 2.81.
Finding the other numbers:
- The first number = 2 * 2.81 ≈ 5.62
- The third number = 3 * 2.81 ≈ 8.43
- The fourth number = 2.81 / 5 ≈ 0.56
Now, let's check if the average of these numbers is indeed 24.75:
Average = (5.62
- 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 assume the second number as 'x'. Based on the given information, we can determine the values of the other three numbers as follows:
- The first number = 2 * x (twice the second number)
- The third number = 3 * x (one-third of the second number)
- The fourth number = x / 5 (one-fifth of the third number)
Now, let's find the average of these four numbers:
Average = (First + Second + Third + Fourth) / 4
24.75 = (2x + x + 3x + x/5) / 4
Simplifying the equation:
24.75 = (11x + x/5) / 4
99 = 55x + x/5
99 = (275x + x) / 5
495 = 276x
x = 495 / 276
x ≈ 1.79
So, the second number is approximately 1.79.
Finding the other numbers:
- The first number = 2 * 1.79 ≈ 3.58
- The third number = 3 * 1.79 ≈ 5.37
- The fourth number = 1.79 / 5 ≈ 0.36
Now, let's check if the average of these numbers is indeed 24.75:
Average = (3.58 + 1.79 + 5.37 + 0.36) / 4
Average ≈ 11.1
Since the calculated average is not equal to 24.75, our assumption for the second number (x) is incorrect.
Let's try a different assumption for the second number.
Let's assume the second number as 'y'. Based on the given information, we can determine the values of the other three numbers as follows:
- The first number = 2 * y (twice the second number)
- The third number = 3 * y (one-third of the second number)
- The fourth number = y / 5 (one-fifth of the third number)
Now, let's find the average of these four numbers:
Average = (First + Second + Third + Fourth) / 4
24.75 = (2y + y + 3y + y/5) / 4
Simplifying the equation:
24.75 = (7y + y/5) / 4
99 = 35y + y/5
99 = (175y + y) / 5
495 = 176y
y = 495 / 176
y ≈ 2.81
So, the second number is approximately 2.81.
Finding the other numbers:
- The first number = 2 * 2.81 ≈ 5.62
- The third number = 3 * 2.81 ≈ 8.43
- The fourth number = 2.81 / 5 ≈ 0.56
Now, let's check if the average of these numbers is indeed 24.75:
Average = (5.62
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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)45b)25c)30d)15Correct answer is option 'A'. Can you explain this answer?
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