Question

Raju and Sarita play a number game. First, each one of them chooses a positive integer independently. Separately, they both multiply their chosen integers by 2, and then subtract 20 from their resultant numbers. Now, each of them has a new number. Then, they divide their respective new numbers by 5. Finally, they added their results and found that the sum is 16. What can be the maximum possible difference between the positive integers chosen by Raju and Sarita?

• A. 67
• B. 58
• C. 49
• D. 40
• E. None of the above

Answer 1

Answer: (B)

58

Answer 2

Let the numbers chosen by Raju and Sarita be 'x' and 'y', respectively.
Step 1: 2x , 2y
Step 2: 2x - 20, 2y - 20
Step 3: 2x - 20/5, 2y-20/5
Step 4: 2x - 20/5 + 2y-20/5 = 16
Thus, 2x + 2y - 40 = 80
x + y = 60
x and y must be as far apart as possible for the difference to be maximum.
Thus, x = 1 and y = 59 or y =1 and x = 59.
The maximum difference = 59 - 1 = 58.
Hence, option B is the correct answer.