Number Puzzle

Question

.The sum old four numbers is 75. If 4 is deducted from the first number, 4 is added to the second number, the third number is divided by 4 and the fourth is multiplied by 4, then all the results are equal. What is the difference between the smallest and the largest of the original numbers?

Answer 1

A+B+C+D=75

A-4=B+4=C/4=4D

A-4=B+4

A=B+8

 

C/4=4D

C=16D

 

A+B+C+D=75

(B+8)+B+16D+D=75

2B+17D+8=75

2B+17D=67

in this equation D can be only 1 or 3 because 2B is even and 5 is too big

let D=3

2B+17*3=67

2B+51=67

2B=16

B=8

B+4=12 and 4D=12

therefore A-4=12 and C/4=12

therefore A=16 and C=48

A=16, B=8, C=48, and D=3

48-3=45