The mess charge made up 24% of a hostel's total yearly fee. Next year the total fee goes up by 15% while the mess charge goes up by 38%. The mess charge will then be what per cent of the total fee?

Take the fee as 100, so the mess charge is 24. Next year the mess charge is $24\times 1.38=33.12$ and the fee is $100\times 1.15=115$, so the share is 33.12/115 = 0.288 = 28.8%. A share rises exactly when the part grows faster than the whole. 33.12% raises the mess charge but leaves the fee at last year's 100 - the base has to move too. 24% assumes the share is fixed. 47% adds and subtracts the rates as points $(24+38-15)$, which mixes shares with growth rates.