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 Scores Range: 
Minimum score: 40
Maximum score: 80
Average score: 60
Test Scores: 
Multiples of 10
Four distinct scores and two equal to the average (60)
Possible test scores: 40, 50, 60, 60, 70, 80
Individual Facts:
Amala's project score is double Koli's, and Koli scored 20 more than Amala in the test.
Amala had the highest aggregate score.
Shyamal scored the second highest in the test, 2 more than Koli, but 2 less than Amala in the aggregate.
Biman scored the second lowest in the test and the lowest in the aggregate.
Mathew scored more than Rini in the project but less than her in the test.
Let's Determine Scores Step-by-Step:
Amala and Koli's Scores:
Let Koli's project score be $P_K$, then Amala's project score is $2P_K$.
Let Amala's test score be $T_A$, then Koli's test score is $T_K = T_A + 20$.
Test Scores Assignment:
To satisfy all conditions, assume possible test scores are 40, 50, 60, 60, 70, 80.
Amala's test score $T_A$ and Koli's $T_K$ should be among these.
Amala's Test Score:
Amala had the highest aggregate score, so $T_A$ is likely one of the higher values.
Try $T_A = 80 \Rightarrow T_K = 100$ (not possible)
Try $T_A = 70 \Rightarrow T_K = 90$ (not possible)
Try $T_A = 60 \Rightarrow T_K = 80$ ✅
Shyamal's Test Score:
Shyamal scored second highest, so $T_S = 70$ (next to Amala's 80), but Amala has 60 in test, so Shyamal must have $T_S = 70$.
Shyamal's aggregate = Amala's aggregate $- 2$.
Biman's Scores:
Biman's test score is second lowest: $T_B = 50$.
Biman had the lowest aggregate score.
Mathew's and Rini's Scores:
Mathew scored more in the project but less in the test compared to Rini.
Remaining test scores are: 40, 60 (one 60 already used by Amala, the other can go to Rini)
So Mathew’s test score = 40, Rini’s = 60
Final Answer:
The person who scored 60 in the test is Rini.
Correct option is (B): 60 Marks.