Five friends Alastair, Bell, Cook, Darren and Eoin appeared in an aptitude test. Alastair scored exactly1/2 of Darrenandrsquo;s score, whosescore was 1/5th more than Cookandrsquo;s score. Eoin scored more than Cook and Darrenandrsquo;s score was 3/2times that of Bellandrsquo;s score. If the average score (arithmetic mean) of the group was 50, what was the range of the scores of the group?a)25b)30c)35d)40e)50Correct answer is option 'D'. Can you explain this answer?

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Five friends Alastair, Bell, Cook, Darren and Eoin appeared in an aptitude test. Alastair scored exactly 1/2 of Darren’s score, whose
score was 1/5^th more than Cook’s score. Eoin scored more than Cook and Darren’s score was 3/2 times that of Bell’s score. If the average score (arithmetic mean) of the group was 50, what was the range of the scores of the group?

a)
25
b)
30
c)
35
d)
40
e)
50

Correct answer is option 'D'. Can you explain this answer?

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Five friends Alastair, Bell, Cook, Darren and Eoin appeared in an apti...

Given:

Relation of scores of Alastair, Bell, Cook, Darren and Eoin in an Aptitude test
- Alastair’s score = ½ * Darren’s Score
- Darren’s Score = Cook’s score + 1/5* Cook’s score =3/2 * Bell’s score
- Eoin’s score = Cook’s score + 2/5* Cook’s score
Average score of the group = 50
- So, total score of the group = 50*5 = 250

To Find: Range of the scores of the group

Range of the score = Highest score – Lowest Score

Approach:

Range of the score = Highest score – Lowest Score
- For finding the highest and the lowest score, we need to find the individual scores of all the 5 people
Let’s assume the score of any one person to be x. Let’s assume that person to be Alastair
- As we are given the relation between the scores of all the 5 people, we will express the scores of other people in terms of x.
Once we get the scores of all the people in terms of x, we know that the sum of their scores is 250.
- So, equating the sum of the scores of all the 5 people to 250 will give us an equation in x, which will give us a unique value of x.

Working out:

Let Alastair’s score be x……….(1)
Darren’s Score
- We know that, Alastair’s score = ½ * Darren’s Score
- So, Darren’s score = 2x………..(2)
Cook’s Score
- Now, we know that Darren’s Score = Cook’s score + 1/5 * Cook’s score

4. Bell’s Score

5. Eoin’s Score

6. Also, sum of all the scores = 250

So, the range of the scores of the group is 40.

Answer D

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Five friends Alastair, Bell, Cook, Darren and Eoin appeared in an aptitude test. Alastair scored exactly1/2 of Darren’s score, whosescore was 1/5th more than Cook’s score. Eoin scored more than Cook and Darren’s score was 3/2times that of Bell’s score. If the average score (arithmetic mean) of the group was 50, what was the range of the scores of the group?a)25b)30c)35d)40e)50Correct answer is option 'D'. Can you explain this answer?

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