The sum of four numbers is 64. If you add 3 to the first number, 3 is subtracted from the 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 the largest and the smallest of the original numbers ?

A. 21

B. 27

C. 32

D. Cannot be determined

E. None of these

Answer: Option C

Solution(By Examveda Team)

Let the four numbers be , A, B, C and D
Let A + 3 = B - 3 = 3C = $$\frac{D}{3}$$ = x
Then,
A = x - 3
B = x + 3
C = $$\frac{x}{3}$$
D = 3x
$$\eqalign{ & \Leftrightarrow A + B + C + D = 64 \cr & \Leftrightarrow \left( {x - 3} \right) + \left( {x + 3} \right) + \frac{x}{3} + 3x = 64 \cr & \Leftrightarrow 5x + \frac{x}{3} = 64 \cr & \Leftrightarrow 16x = 192 \cr & \Leftrightarrow x = 12 \cr} $$
Thus, the numbers are 9, 15, 4 and 36
∴ Required difference :
= (36 - 4)
= 32