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The average of three numbers is 40. The first number is twice the second and the second one is thrice the third number. The difference between the largest and the smallest numbers is?
  • a)
    30
  • b)
    36
  • c)
    46
  • d)
    60
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The average of three numbers is 40. The first number is twice the sec...
Let the third number be x
∴ second number = 3x
First number = 6x
⇒ 10x = 120 ⇒ x = 12
∴ required difference
= 6x - x = 5x = 5 x 12 = 60
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Most Upvoted Answer
The average of three numbers is 40. The first number is twice the sec...
To solve this problem, let's assume the three numbers as follows:

First number = x
Second number = y
Third number = z

Given conditions:
1) The average of three numbers is 40.
(x + y + z) / 3 = 40

2) The first number is twice the second.
x = 2y

3) The second number is thrice the third.
y = 3z

We need to find the difference between the largest and smallest numbers.

------------------------------------------------------------------

Solving the equations:

From equation (2), we can substitute the value of x in terms of y into equation (1):

(2y + y + z) / 3 = 40
(3y + z) / 3 = 40
3y + z = 120

From equation (3), we can substitute the value of y in terms of z into the above equation:

3(3z) + z = 120
9z + z = 120
10z = 120
z = 12

Now, substitute the value of z back into equation (3) to find y:

y = 3z
y = 3(12)
y = 36

Finally, substitute the values of y and z into equation (2) to find x:

x = 2y
x = 2(36)
x = 72

------------------------------------------------------------------

Difference between the largest and smallest numbers:

The largest number is x = 72, and the smallest number is z = 12.

Therefore, the difference between the largest and smallest numbers is:

72 - 12 = 60

Hence, the correct answer is option D) 60.
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The average of three numbers is 40. The first number is twice the second and the second one is thrice the third number. The difference between the largest and the smallest numbers is?a)30b)36c)46d)60Correct answer is option 'D'. Can you explain this answer?
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