An online learning platform offers five courses. The first table gives the number of enrolments (in hundreds) in each course in each quarter of a year. The second table gives the completion rate, i.e. the percentage of that quarter's enrolments that completed the course.
Enrolments (in hundreds)
| Course | Q1 | Q2 | Q3 | Q4 |
|---|---|---|---|---|
| Python | 42 | 48 | 55 | 60 |
| Data Visualisation | 30 | 36 | 33 | 45 |
| Finance | 25 | 28 | 35 | 32 |
| Marketing | 38 | 34 | 40 | 36 |
| Design | 20 | 26 | 30 | 39 |
Completion rate (%)
| Course | Q1 | Q2 | Q3 | Q4 |
|---|---|---|---|---|
| Python | 50 | 45 | 40 | 55 |
| Data Visualisation | 60 | 55 | 60 | 40 |
| Finance | 40 | 50 | 60 | 50 |
| Marketing | 45 | 50 | 35 | 50 |
| Design | 70 | 50 | 60 | 40 |
The fee per enrolment is ₹2,000 for Python, ₹1,500 for Data Visualisation, ₹2,500 for Finance, ₹1,200 for Marketing and ₹1,800 for Design. As a completion incentive, the platform refunds 20% of the fee to every learner who completes a course. Net revenue = total fees collected − refunds paid.
Enrolments (in hundreds)
| Course | Q1 | Q2 | Q3 | Q4 |
|---|---|---|---|---|
| Python | 42 | 48 | 55 | 60 |
| Data Visualisation | 30 | 36 | 33 | 45 |
| Finance | 25 | 28 | 35 | 32 |
| Marketing | 38 | 34 | 40 | 36 |
| Design | 20 | 26 | 30 | 39 |
Completion rate (%)
| Course | Q1 | Q2 | Q3 | Q4 |
|---|---|---|---|---|
| Python | 50 | 45 | 40 | 55 |
| Data Visualisation | 60 | 55 | 60 | 40 |
| Finance | 40 | 50 | 60 | 50 |
| Marketing | 45 | 50 | 35 | 50 |
| Design | 70 | 50 | 60 | 40 |
The fee per enrolment is ₹2,000 for Python, ₹1,500 for Data Visualisation, ₹2,500 for Finance, ₹1,200 for Marketing and ₹1,800 for Design. As a completion incentive, the platform refunds 20% of the fee to every learner who completes a course. Net revenue = total fees collected − refunds paid.
Question 1
Single correct option
In which quarter was the percentage increase in the total enrolments of the platform, over the previous quarter, the highest?
- A. Q2
- B. Q3
- C. Q4
- D. Q2 and Q4 equally
Show answer and solution
Answer: (B) Q3
Total enrolments (hundreds): Q1 = 42 + 30 + 25 + 38 + 20 = 155; Q2 = 48 + 36 + 28 + 34 + 26 = 172; Q3 = 55 + 33 + 35 + 40 + 30 = 193; Q4 = 60 + 45 + 32 + 36 + 39 = 212.
Growth: Q2 over Q1 = 17/155 ≈ 10.97%; Q3 over Q2 = 21/172 ≈ 12.21%; Q4 over Q3 = 19/193 ≈ 9.84%.
The highest growth is in Q3, which also has the largest absolute increase; Q4's increase of 19 is on a bigger base, so its percentage growth is the lowest.
Tip: Compare 17/155, 21/172, 19/193 by noting 21/172 > 1/9 > 17/155 and 19/193 < 1/10.
Growth: Q2 over Q1 = 17/155 ≈ 10.97%; Q3 over Q2 = 21/172 ≈ 12.21%; Q4 over Q3 = 19/193 ≈ 9.84%.
The highest growth is in Q3, which also has the largest absolute increase; Q4's increase of 19 is on a bigger base, so its percentage growth is the lowest.
Tip: Compare 17/155, 21/172, 19/193 by noting 21/172 > 1/9 > 17/155 and 19/193 < 1/10.
Question 2
Numerical answer
What was the total number of learners who completed the Finance course during the year?
Show answer and solution
Answer: 6100
Finance completions = enrolments (in hundreds) × 100 × completion rate.
- Q1: 2500 × 40% = 1000
- Q2: 2800 × 50% = 1400
- Q3: 3500 × 60% = 2100
- Q4: 3200 × 50% = 1600
Total = 1000 + 1400 + 2100 + 1600 = 6100.
Remember the enrolment table is in hundreds — answering 61 is a units error.
- Q1: 2500 × 40% = 1000
- Q2: 2800 × 50% = 1400
- Q3: 3500 × 60% = 2100
- Q4: 3200 × 50% = 1600
Total = 1000 + 1400 + 2100 + 1600 = 6100.
Remember the enrolment table is in hundreds — answering 61 is a units error.
Question 3
Single correct option
Which course had the highest overall completion rate for the year (total completions during the year as a percentage of total enrolments during the year)?
- A. Data Visualisation
- B. Finance
- C. Python
- D. Design
Show answer and solution
Answer: (D) Design
A simple average of the quarterly rates would mislead: Design's average is 55% but its high-rate quarter (Q1) had the fewest enrolments, so a weighted calculation is essential.
Question 4
Numerical answer
In how many of the 20 course-quarter combinations did the number of learners completing the course exceed 2,000?
Show answer and solution
Answer: 5
Data Visualisation peaks at 1980 in Q2 and Q3 — just below 2000 — which is the trap. Answer: 5.
Question 5
Single correct option
Which course generated the second highest net revenue in Q4?
- A. Design
- B. Finance
- C. Data Visualisation
- D. Python
Show answer and solution
Answer: (B) Finance
Net revenue = fee × enrolments × (1 − 0.2 × completion rate). Design has more enrolments than Finance but a lower fee, and the refunds change the gross figures only slightly.
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