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?

The correct answer is 60.

Let the three female students be Amala (A), Koli (K), and Rini (R), and the three male students be Biman (B), Mathew (M), and Shyamal (S).
The project is done in groups of two (one female and one male), and both group members receive the same project score. This means there are exactly three project groups, and thus three distinct project scores, say $P_1$, $P_2$, and $P_3$.

Each of these three scores is shared by two students (one male and one female). Therefore, the project scores of the six students are $P_1,P_1,P_2,P_2,P_3,P_3$.

According to Fact 1:
- The minimum project score is 40.
- The maximum project score is 80.
- The average project score of all students is 60.

We can express the average project score of the 6 students as:
$\frac{2P_1+2P_2+2P_3}{6}=60$
Simplifying this, we get:
$P_1+P_2+P_3=180$

According to Fact 3, Amala's project score, $P\left(A\right)$, was double that of Koli's project score, $P\left(K\right)$:
$P\left(A\right)=2\times P\left(K\right)$

Since the minimum project score is 40:
$P\left(K\right)\ge 40$
This implies:
$P\left(A\right)=2\times P\left(K\right)\ge 80$

Since the maximum possible project score is 80, $P\left(A\right)$ must be exactly 80. Substituting this back gives Koli's project score:
$P\left(K\right)=40$

Let the three project scores corresponding to the three girls be $P\left(A\right)$, $P\left(K\right)$, and Rini's project score, $P\left(R\right)$. Using the sum of the project scores:
$P\left(A\right)+P\left(K\right)+P\left(R\right)=180$
$80+40+P\left(R\right)=180$
$P\left(R\right)=180-120=60$

Thus, Rini's score in the project was 60.