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?

Accepted Answer

B. Let positive integers be $r$ and $s$. $\frac{2r - 20}{5} + \frac{2s - 20}{5} = 16 \implies 2r + 2s - 40 = 80 \implies 2(r+s) = 120 \implies r + s = 60$. Since $r, s$ are positive integers, min value is 1, max is 59. Max difference $|r - s| = |59 - 1| = 58$.

Number Game Maximum Difference

Explanation

Practise this under exam conditions