Explanation:

Let $R$ be the number of sums Ravi got right (solved correctly).\nLet $W$ be the number of sums Ravi got wrong. \nFrom the problem statement, "Ravi got thrice as many sums wrong as he got right": $W = 3R$ \nAlso, "He attempted 72 sums in all":\nThe total number of sums attempted is the sum of correctly solved and wrongly solved sums. $R + W = 72$ \nNow, substitute the first equation ($W = 3R$) into the second equation: $R + (3R) = 72$ $4R = 72$ \nTo find the number of sums solved correctly, divide the total sums by 4: $R = \frac{72}{4}$ $R = 18$ \nSo, Ravi solved 18 sums correctly. \nWe can also find the number of sums he got wrong: $W = 3R = 3 \times 18 = 54$. \nCheck: $R + W = 18 + 54 = 72$. This matches the total number of sums attempted. \nThe question asks: "how many did he solve correctly?" \nAnalyzing the options: (1) 54: This is the number of sums Ravi got wrong. The question asks for sums solved correctly. So, this is incorrect. (2) 36: This value does not correspond to either correctly or wrongly solved sums based on our calculation. So, this is incorrect. (3) 18: This is the number of sums Ravi solved correctly. So, this is correct. (4) 24: This value does not correspond to either correctly or wrongly solved sums based on our calculation. So, this is incorrect. \nThe logically derived answer is 18. Please note that the provided answer key in the document indicates option (1) 54 as correct, which contradicts this derivation. Option (1) represents the number of incorrect answers, not correct ones.