Question:medium

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)

Updated On: Jan 13, 2026
  • 40 Marks
  • 50 Marks
  • 60 Marks
  • 55 Marks
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The Correct Option is A

Solution and Explanation

Given: Project and test scores are between 40 and 80, with an average of 60. Test scores are multiples of 10. All students have unique scores, with the exception of two students who both scored exactly 60 on the test.

Step 1: Assign test scores
The possible distinct test scores are: 40, 50, 60, 70, 80. Since two students scored 60, the complete set of test scores is: 40, 50, 60, 60, 70, 80.

Step 2: Determine Koli's and Amala's project scores
Let Koli's project score be \( x \). Then Amala's project score is \( 2x \). As Amala has the highest project score, \( 2x = 80 \), which means \( x = 40 \). Therefore, Koli's project score is 40, and Amala's project score is 80.

Step 3: Determine Koli's test score
Amala's test score is 60. Koli's test score is 20 more than Amala's, so Koli's test score is \( 60 + 20 = 80 \).

Step 4: Determine Shyamal's test score
Shyamal achieved the second-highest test score, which is 70.

Step 5: Determine Biman's scores
Biman achieved the second-lowest test score, which is 50. Biman has the lowest overall score, implying his project score must also be low. Thus, Biman's project score is 40. Biman's scores: project = 40, test = 50.

Step 6: Determine Mathew's and Rini's scores
The remaining test scores are 40 and 60. Mathew's test score is lower than Rini's, so Mathew's test score is 40 and Rini's is 60. The remaining possible project scores are 60 and 70. Mathew's project score is higher than Rini's. Assigning these, Mathew's project score is 70 and Rini's is 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.

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