What was the weight of the test component?

Students	Test scores (T)	Project scores (P)	Aggregate score (Tx + P{1-x})	Project Pair
Amala
Koli
Rini
Biman
Mathew
Shyamal

According to clue 2,

For the test scores, there are six scores given for six students among which four are distinct and the remaining two are average scores, which is 60. It is also known that the maximum score possible is 80, and the minimum score is 40.

Hence, the distinct scores are 80, 70, 50, and 40 (since all the test scores are multiple of 10), and the remaining two scores are 60, and 60, respectively.

Students	Test scores (T)	Project scores (P)	Aggregate score (Tx + P{1-x})	Project Pair
Amala		80
Koli		40
Rini
Biman
Mathew
Shyamal

Using clue 3,

Amala's score in the project was double that of Koli in the same

The only possibility is Amala's score = 80 and Koli's score = 40 in project.

Students	Test scores (T)	Project scores (P)	Aggregate score (Tx + P{1-x})	Project Pair
Amala	40 / 50 / 60	80
Koli	60 / 70 / 80	40
Rini
Biman
Mathew
Shyamal

Continuing with clue 3,

Koli scored 20 more than Amala in the test

=> In test, Amala can score 40/ 50/ 60

and accordingly, Koli will score 60/ 50/ 80.

Students	Test scores (T)	Project scores (P)	Aggregate score (T*x + P×{1–x})	Project Pair
Amala	40 / 60	80
Koli	60 / 80	40
Rini
Biman
Mathew
Shyamal	70

Clue 3 ,

It is known that Amala had the highest aggregate score

and, Shyamal scored the second highest on the test.

He scored two more than Koli, but two less than Amala in the aggregate.

Hence, the score obtained by Shyamal in the test is 70

=> Koli can't score 70 in the test

=> Amala can't score 50 in the test

Now lets divide it into cases :-

Where first case - The test score of Amala is 40

Students	Test scores (T)	Project scores (P)	Aggregate score (T×x + P×{1−x})	Project Pair
Amala	40	80
Koli	60	40
Rini
Biman
Mathew
Shyamal	70

Therefore, the aggregate score of Amala = 40(1-x) + 80x

Also, aggregate score of Koli will become = 60 (1 - x) + 40 x

Now we know,

Shyamal scored an aggregate which was two more than Koli, but two less than Amala in the aggregate.

=> S = 2 + K = A - 2

(where S - Shyamal; K - Koli; A - Amala)

=> 2 + k = A - 2

=> A - K = 4

putting values of A and K :

40 (1 - x) + 80 x - {60 (1 - x) + 40 x} = 4

=> x = 0.4

Students	Test scores (T)	Project scores (P)	Aggregate score (T×x + P×{1−x})	Project Pair
Amala	60	80
Koli	80	40
Rini
Biman
Mathew
Shyamal	70

Hence, the aggregate score obtained by Amala is 40(1-0.4)+80*4 = 56

But, The Minimum aggregate score of Shyamal is 70(1-0.4)+ 40*0.4 = 58 which is greater than Amala.

Hence, Case 1 is not possible

Therefore case 2 will be correct

i.e., Amala's test score = 60 and Koli's test score will be 80

Students	Test scores (T)	Project scores (P)	Aggregate score (T×0.6 + P×0.4)	Project Pair
Amala	60	80	68
Koli	80	40	64
Rini
Biman
Mathew
Shyamal	70	60	66

Therefore,

60(1-x) + 80x - 80(1-x) + 40x = 4

=> 60+20x = 84 - 40x

=> 60x = 24

=> x = 0.4

Hence, the aggregate score of Amala is 60 (1 - 0.4) + 80*0.4 = 68

=> aggregate score of Shyamal is (68-2) = 66

Hence, the score obtained by Shyamal in Project will be

70 * 0.6 + S * 0.4 = 66

=> 42 + 0.4S = 66

=> S = 60

Students	Test scores (T)	Project scores (P)	Aggregate score (T×0.6 + P×0.4)	Project Pair
Amala	60	80	68
Koli	80	40	64
Rini
Biman	50
Mathew
Shyamal	70	60	66

Clue 5 says, Biman scored the second lowest in the test

=> the score of Biman in the test is 50

Students	Test scores (T)	Project scores (P)	Aggregate score (T×0.6 + P×0.4)	Project Pair
Amala	60	80	68
Koli	80	40	64
Rini	60
Biman	50
Mathew	40
Shyamal	70	60	66

Clue 6 says, Mathew scored more than Rini in the project, but less than her in the test.

=> Rini Scored more than Mathew on the test,

which implies the score obtained by Rini is 60, and the score obtained by Mathew is 40 in the test.

Students	Test scores (T)	Project scores (P)	Aggregate score (T×0.6 + P×0.4)	Project Pair
Amala	60	80	68
Koli	80	40	64
Rini	60	60
Biman	50	40
Mathew	40	80
Shyamal	70	60	66

Similarly, It is also known that Mathew scored more than Rini in the project.

Now, Rini's score = 60 in project

as Koli and Amala already have a score of 40 and 80.

and we know, 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.

Therefore, Mathew's score in project will be greater then 60 which is 80

and biman's score will be 40

Students	Test scores (T)	Project scores (P)	Aggregate score (T×0.6 + P×0.4)	Project Pair
Amala	60	80	68.0
Koli	80	40	64.0
Rini	60	60	60.0
Biman	50	40	46.0
Mathew	40	80	56.0
Shyamal	70	60	66.0

Therefore, aggregate of Rini = 60 * 0.6 + 60* 0.4 = 60

Aggregate of Biman = 50 * 0.6 + 40 * 0.4 = 46

And, aggregate of Mathew = 40 * 0.6 + 80 * 0.4 = 56

Students	Test scores (T)	Project scores (P)	Aggregate score (T×0.6 + P×0.4)	Project Pair
Amala	60	80	68	Amala & Mathew
Koli	80	40	64	Koli & Biman
Rini	60	60	60	Rini & Shyamal
Biman	50	40	46	Koli & Biman
Mathew	40	80	56	Amala & Mathew
Shyamal	70	60	66	Rini & Shyamal

Now we know that 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.

Therefore, the students with the same score in project will be grouped together.

Therefore, the groups formed will be

1. Amala and Mathew

2. Koli and Biman

3. Rini and shyamal

Students	Test scores (T)	Project scores (P)	Aggregate score (T*0.6 + P*0.4)	Project Pair
Amala	60	80	68	Amala & Mathew
Koli	80	40	64	Koli & Biman
Rini	60	60	60	Rini & Shyamal
Biman	50	40	46	Koli & Biman
Mathew	40	80	56	Amala & Mathew
Shyamal	70	60	66	Rini & Shyamal

Hence, the weight of the test component is $0.60$ The correct option is B