The table given below shows the percentage of marks obtained by 6 students S1,…
2021
The table given below shows the percentage of marks obtained by 6 students S1, S2, S3, S4, S5 and S6 in different subjects. Which of the following statement(s) is/are correct? I. If the maximum marks of subject B is 150, then the average marks obtained by all the six students in subject B is 75. II. If the maximum marks of subject A is 120, then the number of students who had scored marks more than 105 is two.
- A.
Only I
- B.
Only II
- C.
Both I and II
- D.
Neither I nor II
Attempted by 39 students.
Show answer & explanation
Correct answer: B
Concept
The table entries are PERCENTAGES, not raw marks. To convert a percentage to actual marks, multiply by the maximum marks: actual mark = (percentage / 100) x maximum marks. The average of the actual marks equals the average percentage multiplied by the maximum marks divided by 100.
Data used
Student | A (%) | B (%) |
|---|---|---|
S1 | 90 | 50 |
S2 | 75 | 80 |
S3 | 90 | 60 |
S4 | 80 | 65 |
S5 | 70 | 75 |
S6 | 65 | 35 |
Statement I (subject B, maximum = 150)
Sum of the six B percentages, then convert the average to marks:
Add the B percentages: 50 + 80 + 60 + 65 + 75 + 35 = 365.
Average percentage in B = 365 / 6 = 60.83% (approximately).
Average actual marks = 60.83% of 150 = (365 / 6) x (150 / 100) = 365 x 1.5 / 6 = 547.5 / 6 = 91.25.
The average actual marks in B is 91.25, not 75. So Statement I is false.
Statement II (subject A, maximum = 120)
Convert each A percentage to marks out of 120 (mark = percentage x 1.2) and count how many exceed 105:
S1: 90% x 1.2 = 108 -> exceeds 105
S2: 75% x 1.2 = 90
S3: 90% x 1.2 = 108 -> exceeds 105
S4: 80% x 1.2 = 96
S5: 70% x 1.2 = 84
S6: 65% x 1.2 = 78
Exactly two students (90% and above, i.e. 90 x 1.2 = 108 > 105) score more than 105. A percentage of 105 / 120 x 100 = 87.5% is the threshold, and only the two 90% scores clear it. So Statement II is true.
Result
Statement I is false and Statement II is true, so only Statement II is correct.
Cross-check
Threshold method for Statement II: scoring more than 105 out of 120 means scoring more than 105/120 = 87.5%. Among the A percentages (90, 75, 90, 80, 70, 65) only the two 90% values exceed 87.5%, confirming the count is two. For Statement I, an average of 75 marks out of 150 would require an average percentage of exactly 50%, but the B average is about 60.83%, well above 50%.