Question

If sum of the four numbers is 64.If 3 is added to first number, 3 is subtracted from second number, the third is multiplied by 3 and the fourth is divided by 3, then all the results are equal.What is the difference between largest and smallest of the original number?

Answer 1

Answer is , original number is 64

Answer 2

The difference between largest and smallest of the original number is 32

Solution:

Let the four numbers be A , B , C , D

3 is added to first number, 3 is subtracted from second number, the third is multiplied by 3 and the fourth is divided by 3

Then,

$A + 3 = B - 3 = C \times 3 = \frac{D}{3} = x$

Thus we get,

$A = x - 3 \\\\B = x + 3 \\\\C = \frac{x}{3} \\\\D = 3x$

Given, sum of the four numbers is 64

$x - 3 + x + 3 + \frac{x}{3} + 3x = 64\\\\5x + \frac{x}{3} = 64\\\\16x = 3 \times 64\\\\x = 12$

Thus the numbers are:

$A = 12 - 3 = 9 \\\\B = 12 + 3 = 15 \\\\C = \frac{12}{3} = 4 \\\\D = 3 \times 12 = 36$

What is the difference between largest and smallest of the original number?

Difference = 36 - 4 = 32

Thus difference between largest and smallest of the original number is 32

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