A food magazine rated six restaurants on four parameters, each on a scale of 1 to 10. The ratings are shown below.
| Restaurant | Food | Service | Ambience | Value |
|---|---|---|---|---|
| Amber | 8 | 7 | 9 | 6 |
| Basil | 9 | 6 | 7 | 7 |
| Clove | 7 | 9 | 8 | 8 |
| Dhaba | 9 | 5 | 4 | 10 |
| Ember | 6 | 8 | 10 | 7 |
| Fennel | 8 | 8 | 6 | 8 |
The overall score of a restaurant is the weighted average of its four ratings. Unless stated otherwise, the weights are: Food 40%, Service 25%, Ambience 15% and Value 20%. Restaurants are ranked in decreasing order of overall score.
| Restaurant | Food | Service | Ambience | Value |
|---|---|---|---|---|
| Amber | 8 | 7 | 9 | 6 |
| Basil | 9 | 6 | 7 | 7 |
| Clove | 7 | 9 | 8 | 8 |
| Dhaba | 9 | 5 | 4 | 10 |
| Ember | 6 | 8 | 10 | 7 |
| Fennel | 8 | 8 | 6 | 8 |
The overall score of a restaurant is the weighted average of its four ratings. Unless stated otherwise, the weights are: Food 40%, Service 25%, Ambience 15% and Value 20%. Restaurants are ranked in decreasing order of overall score.
Question 1
Single correct option
Which restaurant has the highest overall score with the standard weights?
- A. Basil
- B. Clove
- C. Dhaba
- D. Fennel
Show answer and solution
Answer: (B) Clove
Overall = 0.40F + 0.25S + 0.15A + 0.20V:
- Amber: 3.2 + 1.75 + 1.35 + 1.2 = 7.50
- Basil: 3.6 + 1.5 + 1.05 + 1.4 = 7.55
- Clove: 2.8 + 2.25 + 1.2 + 1.6 = 7.85
- Dhaba: 3.6 + 1.25 + 0.6 + 2.0 = 7.45
- Ember: 2.4 + 2.0 + 1.5 + 1.4 = 7.30
- Fennel: 3.2 + 2.0 + 0.9 + 1.6 = 7.70
Clove tops with 7.85, despite having one of the lowest Food ratings — its Service rating of 9 carries a 25% weight.
- Amber: 3.2 + 1.75 + 1.35 + 1.2 = 7.50
- Basil: 3.6 + 1.5 + 1.05 + 1.4 = 7.55
- Clove: 2.8 + 2.25 + 1.2 + 1.6 = 7.85
- Dhaba: 3.6 + 1.25 + 0.6 + 2.0 = 7.45
- Ember: 2.4 + 2.0 + 1.5 + 1.4 = 7.30
- Fennel: 3.2 + 2.0 + 0.9 + 1.6 = 7.70
Clove tops with 7.85, despite having one of the lowest Food ratings — its Service rating of 9 carries a 25% weight.
Question 2
Numerical answer
With the standard weights, how many restaurants have an overall score of at least 7.5?
Show answer and solution
Answer: 4
Scores: Amber 7.50, Basil 7.55, Clove 7.85, Dhaba 7.45, Ember 7.30, Fennel 7.70.
At least 7.5: Amber (exactly 7.50), Basil, Clove, Fennel → 4.
Dhaba misses by 0.05 and Ember by 0.20.
Shortcut: Compare each restaurant with a reference of 7.5 on every parameter; e.g., Dhaba: 0.4(1.5) + 0.25(−2.5) + 0.15(−3.5) + 0.2(2.5) = 0.6 − 0.625 − 0.525 + 0.5 = −0.05.
At least 7.5: Amber (exactly 7.50), Basil, Clove, Fennel → 4.
Dhaba misses by 0.05 and Ember by 0.20.
Shortcut: Compare each restaurant with a reference of 7.5 on every parameter; e.g., Dhaba: 0.4(1.5) + 0.25(−2.5) + 0.15(−3.5) + 0.2(2.5) = 0.6 − 0.625 − 0.525 + 0.5 = −0.05.
Question 3
Single correct option
If the weights are changed to Food 50%, Service 20%, Ambience 10% and Value 20%, which restaurant will be ranked first?
- A. Dhaba
- B. Fennel
- C. Basil
- D. Clove
Show answer and solution
Answer: (A) Dhaba
New overall = 0.5F + 0.2S + 0.1A + 0.2V:
- Amber: 4.0 + 1.4 + 0.9 + 1.2 = 7.5
- Basil: 4.5 + 1.2 + 0.7 + 1.4 = 7.8
- Clove: 3.5 + 1.8 + 0.8 + 1.6 = 7.7
- Dhaba: 4.5 + 1.0 + 0.4 + 2.0 = 7.9
- Ember: 3.0 + 1.6 + 1.0 + 1.4 = 7.0
- Fennel: 4.0 + 1.6 + 0.6 + 1.6 = 7.8
Dhaba now leads with 7.9. Shifting weight from Service and Ambience (Dhaba's weak areas) to Food (its strength) lifts it from fourth to first.
- Amber: 4.0 + 1.4 + 0.9 + 1.2 = 7.5
- Basil: 4.5 + 1.2 + 0.7 + 1.4 = 7.8
- Clove: 3.5 + 1.8 + 0.8 + 1.6 = 7.7
- Dhaba: 4.5 + 1.0 + 0.4 + 2.0 = 7.9
- Ember: 3.0 + 1.6 + 1.0 + 1.4 = 7.0
- Fennel: 4.0 + 1.6 + 0.6 + 1.6 = 7.8
Dhaba now leads with 7.9. Shifting weight from Service and Ambience (Dhaba's weak areas) to Food (its strength) lifts it from fourth to first.
Question 4
Numerical answer
With the standard weights, by at least how many points must Dhaba's Service rating increase (ratings remain integers, all other ratings unchanged) for Dhaba to have the strictly highest overall score?
Show answer and solution
Answer: 2
Dhaba's current score is 7.45; the leader is Clove with 7.85. Each extra Service point adds 0.25 to Dhaba's score.
- +1 point: 7.70 < 7.85 (still behind Clove)
- +2 points: 7.95 > 7.85 ✓
So the minimum increase is 2 points (Service from 5 to 7).
Tip: Required gain = 7.85 − 7.45 = 0.40; 0.40/0.25 = 1.6, so round up to 2 because ratings are integers and the lead must be strict.
- +1 point: 7.70 < 7.85 (still behind Clove)
- +2 points: 7.95 > 7.85 ✓
So the minimum increase is 2 points (Service from 5 to 7).
Tip: Required gain = 7.85 − 7.45 = 0.40; 0.40/0.25 = 1.6, so round up to 2 because ratings are integers and the lead must be strict.
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