Proportional scoring in an innings: The highest score equals 3/11 of the team total T. The second-highest equals 3/11 of the remainder after removing the highest. If the difference between these two scores is 9 runs, what is the total score T?

Introduction / Context:This question involves expressing parts of a total in fractions and then comparing those parts. It is a clean application of linear relationships and fraction arithmetic, typical in quantitative reasoning sections.

Given Data / Assumptions:

• Highest score H = (3/11) * T.
• Remainder after removing H: T − H = T − 3T/11 = 8T/11.
• Second-highest N = (3/11) * (8T/11) = 24T/121.
• Difference H − N = 9.

Concept / Approach:Form expressions for both scores, subtract them, and solve for T. The denominators are manageable (11 and 121), making exact manipulation easy and reliable.

Step-by-Step Solution:H − N = (3T/11) − (24T/121).Common denominator 121: H − N = (33T − 24T)/121 = 9T/121.Set 9T/121 = 9 ⇒ T = 121.

Verification / Alternative check:Compute H = 3*121/11 = 33; N = 24*121/121 = 24; difference = 9, as required.

Why Other Options Are Wrong:99, 110, 132, and 143 do not yield a 9-run difference with the specified fractional structure.

Common Pitfalls:Taking the second-highest as 3/11 of T instead of the remainder; arithmetic slips in converting 3/11 of 8/11 T.

Final Answer:121