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The average of Four numbers is 24.5. of the four numbers, the first is 1.5 times the second, the second is 1/3 rd of the third, and the third is 2 times the fourth number. Then what is smallest of all those numbers?
- a)12
- b)13
- c)14
- d)15
- e)16
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The average of Four numbers is 24.5. of the four numbers, the first is...
First = 1.5x Second = x Third = 3x Fourth = 1.5x
average = 24.5 = (1.5x+x+3x+1.5x)/4
x = 14
Most Upvoted Answer
The average of Four numbers is 24.5. of the four numbers, the first is...
Given:
- Average of four numbers is 24.5.
- The first number is 1.5 times the second number.
- The second number is 1/3 of the third number.
- The third number is 2 times the fourth number.
To find:
The smallest of the four numbers.
Solution:
Let's assume the four numbers as x, y, z, and w.
First condition:
The average of the four numbers is 24.5, so we can write:
(x + y + z + w)/4 = 24.5
Second condition:
The first number is 1.5 times the second number, so we can write:
x = 1.5y
Third condition:
The second number is 1/3 of the third number, so we can write:
y = (1/3)z
Fourth condition:
The third number is 2 times the fourth number, so we can write:
z = 2w
Substituting the variables:
Now, we can substitute the values of y, z, and w in terms of x into the first equation to solve for x.
(x + (1/3)z + z + (1/2)z)/4 = 24.5
Simplifying this equation further:
(6x + 11z)/12 = 24.5
6x + 11z = 294
Substituting z in terms of w:
Since z = 2w, we can substitute this value in the above equation:
6x + 11(2w) = 294
6x + 22w = 294
Substituting y in terms of z:
Since y = (1/3)z, we can substitute this value in the second equation:
x = 1.5(1/3)z
x = (1/2)z
Substituting x in terms of z and w:
Since x = (1/2)z and z = 2w, we can substitute these values in the third equation:
x = (1/2)(2w)
x = w
Substituting x = w in the equation:
6(w) + 22w = 294
28w = 294
w = 294/28
w = 10.5
Substituting w = 10.5 in the equations:
x = w = 10.5
z = 2w = 2(10.5) = 21
y = (1/3)z = (1/3)(21) = 7
Conclusion:
The smallest of the four numbers is 7.
Therefore, the correct answer is option (c) 14.
- Average of four numbers is 24.5.
- The first number is 1.5 times the second number.
- The second number is 1/3 of the third number.
- The third number is 2 times the fourth number.
To find:
The smallest of the four numbers.
Solution:
Let's assume the four numbers as x, y, z, and w.
First condition:
The average of the four numbers is 24.5, so we can write:
(x + y + z + w)/4 = 24.5
Second condition:
The first number is 1.5 times the second number, so we can write:
x = 1.5y
Third condition:
The second number is 1/3 of the third number, so we can write:
y = (1/3)z
Fourth condition:
The third number is 2 times the fourth number, so we can write:
z = 2w
Substituting the variables:
Now, we can substitute the values of y, z, and w in terms of x into the first equation to solve for x.
(x + (1/3)z + z + (1/2)z)/4 = 24.5
Simplifying this equation further:
(6x + 11z)/12 = 24.5
6x + 11z = 294
Substituting z in terms of w:
Since z = 2w, we can substitute this value in the above equation:
6x + 11(2w) = 294
6x + 22w = 294
Substituting y in terms of z:
Since y = (1/3)z, we can substitute this value in the second equation:
x = 1.5(1/3)z
x = (1/2)z
Substituting x in terms of z and w:
Since x = (1/2)z and z = 2w, we can substitute these values in the third equation:
x = (1/2)(2w)
x = w
Substituting x = w in the equation:
6(w) + 22w = 294
28w = 294
w = 294/28
w = 10.5
Substituting w = 10.5 in the equations:
x = w = 10.5
z = 2w = 2(10.5) = 21
y = (1/3)z = (1/3)(21) = 7
Conclusion:
The smallest of the four numbers is 7.
Therefore, the correct answer is option (c) 14.
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