Cricket scoring logic: The highest score in an innings was 3/11 of the total, and the next highest was 3/11 of the remainder after removing the highest. If these two scores differ by 18, find the total score.

Introduction / Context:This word problem tests proportional reasoning and careful setup of fractional parts of a whole. We translate the narrative into algebra involving the total score T and compute the two specified top scores.

Given Data / Assumptions:

• Highest score H = (3/11) * T.
• Remainder after removing H is T − H.
• Next highest N = (3/11) * (T − H).
• Difference H − N = 18 (highest exceeds next highest).

Concept / Approach:Express both H and N in terms of T, then take their difference and equate it to 18. Solve for T using straightforward linear algebra. Fractions must be handled carefully; adopting a common denominator helps avoid mistakes.

Step-by-Step Solution:

Verification / Alternative check:Compute scores: H = (3/11)*242 = 66; N = (24/121)*242 = 48; difference = 18, matching the condition.

Why Other Options Are Wrong:244, 294, 255, and 231 do not satisfy the difference equation H − N = 18 when substituted.

Common Pitfalls:Using 3/11 of the total again for the second score instead of 3/11 of the remainder, or subtracting in the wrong order leading to a negative difference.

Final Answer:242