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.

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What was Rini's score in the project?

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.

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What was Rini's score in the project?

Accepted Answer

To determine Rini's score in the project, we analyze each piece of information step by step:

1. **Project Scores (Facts 1 & 3):**
   - The possible project scores are **40**, **60**, and **80**, as per Fact 1.
   - Amala's project score is **double that of Koli's** (Fact 3). Hence:  
     - If Koli's project score = **40**, then Amala's = **80**.
     - This satisfies Fact 3 since Amala has the highest aggregate score.

2. **Test Scores (Facts 2 & 4):**
   - The possible test scores are multiples of **10**, with four distinct scores and two equal to **60** (the average).  
   - Let Amala's test score = **80** (highest), as she has the highest aggregate score.
   - Koli's test score = **60**, since it is **20 less than Amala's** (Fact 3).
   - Shyamal's test score = **62**, as it is **two more than Koli's** (Fact 4).
   - Biman’s lowest

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