Study the given table and answer the question that follows. The table gives…
2023
Study the given table and answer the question that follows. The table gives the number of graduate students enrolled in 4 different colleges A, B, C and D in a city over the years 2010 to 2014, and also the number of students who passed in the final examination during these years.
Find the percentage of students who passed from college B for all the years put together, taken with respect to the number of students enrolled in college B during all those years (rounded to 2 decimals).
Answer: A. 94.92% — Concept: A percentage compares a part with a whole through the relation percentage = (part / whole) x 100. When one single figure is wanted for several years…
- A.
94.92%
- B.
94.98%
- C.
94.95%
- D.
94.96%
Show answer & explanation
Correct answer: A
Concept: A percentage compares a part with a whole through the relation percentage = (part / whole) x 100. When one single figure is wanted for several years taken together, the comparison must be built from totals: the parts are added up, the wholes are added up, and only that one combined ratio is turned into a percentage. The average of the separate yearly percentages is a different quantity and does not answer this kind of question.
Application: the required percentage concerns college B alone, so only the 'B' row of the table is used. Its year-wise enrolment and pass counts are:
Year | Enrolled | Passed |
|---|---|---|
2010 | 550 | 530 |
2011 | 450 | 420 |
2012 | 600 | 550 |
2013 | 650 | 620 |
2014 | 700 | 680 |
Total (2010 to 2014) | 2950 | 2800 |
Add the enrolment figures: 550 + 450 + 600 + 650 + 700 = 2950 students enrolled in college B over the five years.
Add the pass figures: 530 + 420 + 550 + 620 + 680 = 2800 students passed from college B over the same five years.
Apply the percentage relation to these totals: required percentage = (2800 / 2950) x 100.
Simplify the ratio by dividing numerator and denominator by 50: 2800 / 2950 = 56 / 59.
Carry out the division: 56 / 59 = 0.949152542..., so (2800 / 2950) x 100 = 94.9152542...%.
Round to two decimal places: the thousandths digit is 5 and further non-zero digits follow it, so the hundredths digit is raised and 94.9152542...% becomes 94.92%.
Cross-check: reversing the calculation, 94.92% of 2950 is 0.9492 x 2950 = 2800.14, which returns the 2800 students who passed to within the rounding tolerance, confirming the aggregate ratio. A second check shows why the totals had to be summed before dividing: the year-wise pass percentages for college B are 96.36%, 93.33%, 91.67%, 95.38% and 97.14%, and their plain average is 94.78% - close to, but not the same as, the combined 94.92% obtained from the five-year totals.