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Highest mark: 45
Lowest mark: 15

'5' is added to \(\frac{1}{3}\) of marks in semi-annual exam:

=> New highest score: \(\frac{1}{3}\) * 45 + 5 = 15 + 5 = 20

=> New lowest score: \(\frac{1}{3}\) * 15 + 5 = 5 + 5 = 10

=> Old range: 45 - 15 = 30
=> New range: 20 - 10 = 10

Difference between Old and new range: 30 - 10 = 20

Answer C
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A quick conceptual shortcut here is to remember that adding a constant (like the 5) doesn't change the range, but multiplying the scores by 1/3 also multiplies the range by 1/3. So, the new range is just 30x(1/3) = 10. The difference is 30 - 10 = 20.
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