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 Mathew's score in the test?(This Question was asked as TITA)

• A. 40 Marks
• B. 50 Marks
• C. 60 Marks
• D. 55 Marks

Answer 1

The Correct Option is A

Given: Project and test scores range from 40 to 80, average 60. Test scores are multiples of 10. Each student has distinct scores, except two students scoring exactly 60 in test.

Step 1: Assign test scores 
Possible distinct scores: 40, 50, 60, 70, 80
Two students score exactly 60. So, test scores: 40, 50, 60, 60, 70, 80

Step 2: Koli and Amala
Let Koli’s project score be \( x \), then Amala’s is \( 2x \)
Since Amala has the highest project score, \( 2x = 80 \Rightarrow x = 40 \)
So, Koli: project = 40, Amala: project = 80

Step 3: Koli's test score
Amala’s test score is 60. Koli’s test score is 20 more → \( 60 + 20 = 80 \)
So, Koli’s test = 80

Step 4: Shyamal's test score
Shyamal scored second-highest in test ⇒ 70

Step 5: Biman's scores
Biman scored second-lowest in test ⇒ 50
Biman has the lowest overall score. So his project must also be low: 40
Biman: project = 40, test = 50

Step 6: Mathew and Rini
Test scores left: 40 and 60
Mathew’s test score is less than Rini’s ⇒ Mathew = 40, Rini = 60
Mathew’s project score is higher than Rini’s. Possible project scores left: 60 and 70
Assign: Mathew project = 70, Rini = 60

Step 7: Verify all scores
 

• Koli: (40 + 80)/2 = 60
• Amala: (80 + 60)/2 = 70
• Shyamal: (60 + 70)/2 = 65
• Biman: (40 + 50)/2 = 45
• Rini: (60 + 60)/2 = 60
• Mathew: (70 + 40)/2 = 55

 

Answer: Mathew’s test score is 40 marks.