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Mr. Rajan takes three numbers. Out of these three numbers, the second is twice the third and the first is twice the second. The average of the reciprocal of the numbers is 7/36. Find the sum of all the three numbers.
- a)21
- b)18
- c)36
- d)Can't be determined
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Mr. Rajan takes three numbers. Out of these three numbers, the second ...
Let the three numbers be x, y and z.
Now, according to the question,
y = 2z and x = 2y = 4z
Also, average of the reciprocal = 7/36
Now, according to the question,
y = 2z and x = 2y = 4z
Also, average of the reciprocal = 7/36
After solving this, we get:
z = 3
Then,
x = 12
y = 6
Sum of all three numbers = 21
z = 3
Then,
x = 12
y = 6
Sum of all three numbers = 21
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Community Answer
Mr. Rajan takes three numbers. Out of these three numbers, the second ...
To solve this problem, let's assume the three numbers as follows:
Let the third number be x.
Then, the second number will be 2x (twice the third number).
And the first number will be 2(2x) = 4x (twice the second number).
The average of the reciprocal of the numbers is given as 7/36. So, we can write the equation as:
(1/x + 1/(2x) + 1/(4x)) / 3 = 7/36
Simplifying the equation, we get:
(4 + 2 + 1) / (4x) = 7/36
7 / (4x) = 7/36
From this equation, we can conclude that 4x = 36, which gives us x = 9.
Now, we can find the three numbers:
First number = 4x = 4(9) = 36
Second number = 2x = 2(9) = 18
Third number = x = 9
The sum of all three numbers is 36 + 18 + 9 = 63.
Therefore, the correct answer is option A) 63.
Let the third number be x.
Then, the second number will be 2x (twice the third number).
And the first number will be 2(2x) = 4x (twice the second number).
The average of the reciprocal of the numbers is given as 7/36. So, we can write the equation as:
(1/x + 1/(2x) + 1/(4x)) / 3 = 7/36
Simplifying the equation, we get:
(4 + 2 + 1) / (4x) = 7/36
7 / (4x) = 7/36
From this equation, we can conclude that 4x = 36, which gives us x = 9.
Now, we can find the three numbers:
First number = 4x = 4(9) = 36
Second number = 2x = 2(9) = 18
Third number = x = 9
The sum of all three numbers is 36 + 18 + 9 = 63.
Therefore, the correct answer is option A) 63.
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