UGC NET CSE | June 2011 | Part 2 | Question: 2

Question

The circumference of the two concentric disks are divided into $100$ sections each. For the outer disk, $100$ of the sections are painted red and $100$ of the sections are painted blue. For the inner disk, the sections are painted red and blue in an arbitrary manner. It is possible to align the two disks so that

• A. $100$ or more
• B. $125$ or more
• C. $150$ or more
• D. $175$ or more

of the sections on the inner disks have their colours matched with the corresponding section on outer disk.

Answer 1

inner disk.
Consider a half with r reds.
Half1 = r reds and 100-r whites
Half2 = R -r reds and 100-(R-r) = 100 - R +r whites.

If r > = R - r, match half1 with Red half of outer disk.
Total matching = r + 100 - R + r = 100 - R + 2r
Now r >= R - r => 2r - R >= 0
Total matching = 100 - R + 2r >= 100