Five friends — P, Q, R, S and T — had breakfast at a South Indian restaurant. The menu had only five items:
| Item | Price (₹) |
|---|---|
| Masala Dosa | 90 |
| Idli | 60 |
| Vada | 50 |
| Uttapam | 110 |
| Filter Coffee | 40 |
Each friend ordered at least two and at most four different items, and no one ordered more than one plate or cup of any item. Each friend received a separate bill for exactly the items he or she ordered (before any tax or waiver). The following is also known:
1. P's bill was ₹180.
2. S's bill was ₹100, and it was strictly smaller than every other friend's bill.
3. R and T had equal bills, and Q's bill was ₹20 less than R's.
4. The five bills added up to ₹980.
5. Exactly four of the friends ordered Filter Coffee; Q was not one of them.
6. Exactly two of the friends ordered Uttapam.
7. R did not order Vada.
| Item | Price (₹) |
|---|---|
| Masala Dosa | 90 |
| Idli | 60 |
| Vada | 50 |
| Uttapam | 110 |
| Filter Coffee | 40 |
Each friend ordered at least two and at most four different items, and no one ordered more than one plate or cup of any item. Each friend received a separate bill for exactly the items he or she ordered (before any tax or waiver). The following is also known:
1. P's bill was ₹180.
2. S's bill was ₹100, and it was strictly smaller than every other friend's bill.
3. R and T had equal bills, and Q's bill was ₹20 less than R's.
4. The five bills added up to ₹980.
5. Exactly four of the friends ordered Filter Coffee; Q was not one of them.
6. Exactly two of the friends ordered Uttapam.
7. R did not order Vada.
Question 1
Single correct option
Which two friends ordered Uttapam?
- A. P and R
- B. R and T
- C. Q and T
- D. Q and R
Show answer and solution
Answer: (D) Q and R
Deduction: from (3) and (4), 180 + 100 + R + R + (R − 20) = 980, so R = T = ₹240 and Q = ₹220.
- S (₹100, at least two items): only Idli + Coffee = 100 works.
- P (₹180): only Dosa + Vada + Coffee works.
- Q (₹220, no coffee): only Idli + Vada + Uttapam works.
- R and T (₹240 each): the options are {Dosa, Uttapam, Coffee} or {Dosa, Idli, Vada, Coffee}. R cannot have Vada, so R = Dosa + Uttapam + Coffee and T = Dosa + Idli + Vada + Coffee.
Check: Coffee is ordered by P, R, S, T (4 ✓); Uttapam by Q, R (2 ✓).
| Friend | Items | Bill (₹) |
|---|---|---|
| P | Dosa, Vada, Coffee | 180 |
| Q | Idli, Vada, Uttapam | 220 |
| R | Dosa, Uttapam, Coffee | 240 |
| S | Idli, Coffee | 100 |
| T | Dosa, Idli, Vada, Coffee | 240 |
Uttapam was ordered by Q and R.
- S (₹100, at least two items): only Idli + Coffee = 100 works.
- P (₹180): only Dosa + Vada + Coffee works.
- Q (₹220, no coffee): only Idli + Vada + Uttapam works.
- R and T (₹240 each): the options are {Dosa, Uttapam, Coffee} or {Dosa, Idli, Vada, Coffee}. R cannot have Vada, so R = Dosa + Uttapam + Coffee and T = Dosa + Idli + Vada + Coffee.
Check: Coffee is ordered by P, R, S, T (4 ✓); Uttapam by Q, R (2 ✓).
| Friend | Items | Bill (₹) |
|---|---|---|
| P | Dosa, Vada, Coffee | 180 |
| Q | Idli, Vada, Uttapam | 220 |
| R | Dosa, Uttapam, Coffee | 240 |
| S | Idli, Coffee | 100 |
| T | Dosa, Idli, Vada, Coffee | 240 |
Uttapam was ordered by Q and R.
Question 2
Numerical answer
How many of the five friends ordered Vada?
Show answer and solution
Answer: 3
Using the final grid (P: Dosa, Vada, Coffee; Q: Idli, Vada, Uttapam; R: Dosa, Uttapam, Coffee; S: Idli, Coffee; T: Dosa, Idli, Vada, Coffee), Vada was ordered by P, Q and T, so 3 friends.
The key step is R = T = ₹240: of the two ₹240 combinations, clue 7 rules out the one with Vada for R, forcing it onto T.
The key step is R = T = ₹240: of the two ₹240 combinations, clue 7 rules out the one with Vada for R, forcing it onto T.
Question 3
Numerical answer
What was the total amount (in ₹) spent by the group on Masala Dosa?
Show answer and solution
Answer: 270
Masala Dosa was ordered by P, R and T (see the grid: P = Dosa + Vada + Coffee, R = Dosa + Uttapam + Coffee, T = Dosa + Idli + Vada + Coffee).
Total = 3 × 90 = ₹270.
Check on the whole grid: Dosa 270 + Idli 180 + Vada 150 + Uttapam 220 + Coffee 160 = 980, which matches clue 4.
Total = 3 × 90 = ₹270.
Check on the whole grid: Dosa 270 + Idli 180 + Vada 150 + Uttapam 220 + Coffee 160 = 980, which matches clue 4.
Question 4
Single correct option
The restaurant runs an offer: on any bill of ₹200 or more that includes Filter Coffee, the price of one coffee is waived. After the waiver, 5% GST is added to every bill. What is the total amount paid by the five friends?
- A. ₹1,029
- B. ₹945
- C. ₹900
- D. ₹987
Show answer and solution
Answer: (B) ₹945
Bills of ₹200 or more: Q (220), R (240), T (240). Q did not order coffee, so the waiver applies only to R and T, and each saves ₹40.
Pre-tax total = 980 − 80 = ₹900. With 5% GST: 900 × 1.05 = ₹945.
Traps: ₹1,029 ignores the waiver (980 × 1.05); ₹987 applies the waiver to only one bill (940 × 1.05); ₹900 forgets the GST.
Pre-tax total = 980 − 80 = ₹900. With 5% GST: 900 × 1.05 = ₹945.
Traps: ₹1,029 ignores the waiver (980 × 1.05); ₹987 applies the waiver to only one bill (940 × 1.05); ₹900 forgets the GST.
Question 5
Single correct option
Which of the following statements is FALSE?
- A. T ordered Idli.
- B. Every item on the menu was ordered by at least two friends.
- C. P and R had exactly two items in common.
- D. S ordered Vada.
Show answer and solution
Answer: (D) S ordered Vada.
From the grid:
- T ordered Idli: true.
- Every item was ordered by at least two friends: Dosa 3, Idli 3, Vada 3, Uttapam 2, Coffee 4, so true.
- P (Dosa, Vada, Coffee) and R (Dosa, Uttapam, Coffee) have exactly two items in common: true.
- S ordered Vada: false. S's ₹100 bill with at least two items can only be Idli + Coffee.
Answer: the fourth statement.
- T ordered Idli: true.
- Every item was ordered by at least two friends: Dosa 3, Idli 3, Vada 3, Uttapam 2, Coffee 4, so true.
- P (Dosa, Vada, Coffee) and R (Dosa, Uttapam, Coffee) have exactly two items in common: true.
- S ordered Vada: false. S's ₹100 bill with at least two items can only be Idli + Coffee.
Answer: the fourth statement.
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