Question

There are only three female students - Amala, Koli and Rini - and only three male students - Biman, Mathew and Shyamal - in a course. The course has two evaluation components, a project and a test. The aggregate score in the course is a weighted average of the two components, with the weights being positive and adding to 1 . 
The projects are done in groups of two, with each group consisting of a female and a male student. Both the group members obtain the same score in the project. 
The following additional facts are known about the scores in the project and the test.
1. The minimum, maximum and the average of both project and test scores were identical – 40, 80 and 60 , respectively. 
2. The test scores of the students were all multiples of 10 ; four of them were distinct and the remaining two were equal to the average test scores.
3. Amala's score in the project was double that of Koli in the same, but Koli scored 20 more than Amala in the test. Yet Amala had the highest aggregate score. 
4. Shyamal scored the second highest in the test. He scored two more than Koli, but two less than Amala in the aggregate. 
5. Biman scored the second lowest in the test and the lowest in the aggregate. 
6. Mathew scored more than Rini in the project, but less than her in the test.
What was Rini's score in the project?(This Question was asked as TITA)

• A. 45 Marks
• B. 60 Marks
• C. 70 Marks
• D. 80 Marks

Answer 1

The Correct Option is B

Project and Test Score Parameters:
Minimum score: 40
Maximum score: 80
Average score: 60
Test Score Distribution:
Scores are multiples of 10.
There are four distinct scores and two scores equal to the average (60).
Possible test scores: 40, 50, 60, 60, 70, 80
Individual Performance Data:
Amala's project score is twice Koli's. Koli's test score is 20 points higher than Amala's.
Amala achieved the highest overall aggregate score.
Shyamal had the second-highest test score. His aggregate score was 2 points less than Amala's, and his test score was 2 points more than Koli's, but 2 points less than Amala's. (Correction: The text states Shyamal scored 2 more than Koli, but 2 less than Amala in aggregate. The test score detail seems to conflict with the aggregate detail. Re-evaluating based on the aggregate calculation later.)
Biman achieved the second-lowest test score and the lowest aggregate score.
Mathew's project score exceeded Rini's, while his test score was lower than Rini's.
Score Determination Process:
Amala and Koli's Scores Analysis:
Let $P_K$ represent Koli's project score; Amala's project score is $2P_K$.
Let $T_A$ represent Amala's test score; Koli's test score is $T_K = T_A + 20$.
Test Score Allocation:
To fulfill all conditions, the available test scores are 40, 50, 60, 60, 70, 80.
Amala's and Koli's test scores ($T_A, T_K$) must be chosen from this set.
Amala's Test Score Determination:
Amala's highest aggregate suggests $T_A$ should be a high value.
Attempt 1: $T_A = 80 \Rightarrow T_K = 80 + 20 = 100$ (Invalid score).
Attempt 2: $T_A = 70 \Rightarrow T_K = 70 + 20 = 90$ (Invalid score).
Attempt 3: $T_A = 60 \Rightarrow T_K = 60 + 20 = 80$. Both scores (60, 80) are valid and available. This is a potential assignment.
Shyamal's Test Score Determination:
Shyamal's aggregate is 2 less than Amala's. Based on the successful assignment for Amala ($T_A=60$) and the overall score distribution, Shyamal's test score should be the next highest available distinct score after Amala's. The phrasing "Shyamal scored the second highest in the test" implies a comparison to *all* test scores, not just distinct ones. Given Amala has 60, and the highest distinct scores are 80 and 70, Shyamal's test score is likely 70, making his aggregate 2 less than Amala's (assuming Amala's aggregate calculation uses her test score of 60). Let's proceed with $T_S = 70$.
Biman's Scores Determination:
Biman's test score is the second lowest: $T_B = 50$.
Biman's aggregate score is the lowest.
Mathew's and Rini's Scores Determination:
Mathew's project score is higher than Rini's, but his test score is lower.
Remaining test scores to be assigned: 40, 60 (one 60 was assigned to Amala, the other 60 is available). The remaining distinct scores are 40 and 60.
To satisfy Mathew scoring less than Rini in the test, Mathew's test score is 40, and Rini's test score is 60.
Conclusion:
The individual who scored 60 in the test is Rini.
Correct option is (B): 60 Marks.