Five students — Anil, Bela, Chirag, Dia and Esha — took examinations in Maths, Physics and Chemistry. In each subject the five were ranked 1 (best) to 5 (worst) with no ties. A student's *total* is the sum of his or her three ranks; the student with the lowest total is placed first overall, and if two students have the same total, the one with the better Maths rank is placed higher.
The following is known:
1. No student obtained the same rank in any two subjects.
2. Anil was ranked 1 in Physics but 5 in Chemistry.
3. The student ranked 1 in Maths was ranked 3 in Chemistry.
4. Chirag was ranked 5 in Maths, and in Physics he was ranked immediately above Esha.
5. Esha was ranked 2 in Chemistry.
6. Dia had a better Maths rank than Anil, but a worse Physics rank than Bela.
7. Bela and Dia had the same total, and every other student had a higher total than them.
The following is known:
1. No student obtained the same rank in any two subjects.
2. Anil was ranked 1 in Physics but 5 in Chemistry.
3. The student ranked 1 in Maths was ranked 3 in Chemistry.
4. Chirag was ranked 5 in Maths, and in Physics he was ranked immediately above Esha.
5. Esha was ranked 2 in Chemistry.
6. Dia had a better Maths rank than Anil, but a worse Physics rank than Bela.
7. Bela and Dia had the same total, and every other student had a higher total than them.
Question 1
Single correct option
Who was ranked 2 in Maths?
- A. Anil
- B. Bela
- C. Esha
- D. Dia
Show answer and solution
Answer: (D) Dia
Fixed at once: Anil – Physics 1, Chemistry 5; Esha – Chemistry 2; Chirag – Maths 5. Chirag cannot also be 5th in Physics (clue 1), so (Chirag, Esha) in Physics is (2, 3) or (3, 4). The Maths topper is 3rd in Chemistry, so it is Bela or Dia (Anil, Esha, Chirag are excluded). Dia is behind Bela in Physics. Clues 1–6 still allow nine grids (e.g. with Dia topping Maths, totals come out as Anil 8 or Bela 7 — lower than Dia's), and clue 7 — Bela and Dia tie for the strictly lowest total — survives in exactly one:
| Student | Maths | Physics | Chemistry | Total |
|---|---|---|---|---|
| Anil | 3 | 1 | 5 | 9 |
| Bela | 1 | 4 | 3 | 8 |
| Chirag | 5 | 2 | 4 | 11 |
| Dia | 2 | 5 | 1 | 8 |
| Esha | 4 | 3 | 2 | 9 |
Rank 2 in Maths: Dia.
| Student | Maths | Physics | Chemistry | Total |
|---|---|---|---|---|
| Anil | 3 | 1 | 5 | 9 |
| Bela | 1 | 4 | 3 | 8 |
| Chirag | 5 | 2 | 4 | 11 |
| Dia | 2 | 5 | 1 | 8 |
| Esha | 4 | 3 | 2 | 9 |
Rank 2 in Maths: Dia.
Question 2
Numerical answer
What is Chirag's total?
Show answer and solution
Answer: 11
Fixed at once: Anil – Physics 1, Chemistry 5; Esha – Chemistry 2; Chirag – Maths 5. Chirag cannot also be 5th in Physics (clue 1), so (Chirag, Esha) in Physics is (2, 3) or (3, 4). The Maths topper is 3rd in Chemistry, so it is Bela or Dia (Anil, Esha, Chirag are excluded). Dia is behind Bela in Physics. Clues 1–6 still allow nine grids (e.g. with Dia topping Maths, totals come out as Anil 8 or Bela 7 — lower than Dia's), and clue 7 — Bela and Dia tie for the strictly lowest total — survives in exactly one:
| Student | Maths | Physics | Chemistry | Total |
|---|---|---|---|---|
| Anil | 3 | 1 | 5 | 9 |
| Bela | 1 | 4 | 3 | 8 |
| Chirag | 5 | 2 | 4 | 11 |
| Dia | 2 | 5 | 1 | 8 |
| Esha | 4 | 3 | 2 | 9 |
Chirag: 5 + 2 + 4 = 11.
| Student | Maths | Physics | Chemistry | Total |
|---|---|---|---|---|
| Anil | 3 | 1 | 5 | 9 |
| Bela | 1 | 4 | 3 | 8 |
| Chirag | 5 | 2 | 4 | 11 |
| Dia | 2 | 5 | 1 | 8 |
| Esha | 4 | 3 | 2 | 9 |
Chirag: 5 + 2 + 4 = 11.
Question 3
Single correct option
Who was placed third overall?
- A. Anil
- B. Esha
- C. Dia
- D. Chirag
Show answer and solution
Answer: (A) Anil
Fixed at once: Anil – Physics 1, Chemistry 5; Esha – Chemistry 2; Chirag – Maths 5. Chirag cannot also be 5th in Physics (clue 1), so (Chirag, Esha) in Physics is (2, 3) or (3, 4). The Maths topper is 3rd in Chemistry, so it is Bela or Dia (Anil, Esha, Chirag are excluded). Dia is behind Bela in Physics. Clues 1–6 still allow nine grids (e.g. with Dia topping Maths, totals come out as Anil 8 or Bela 7 — lower than Dia's), and clue 7 — Bela and Dia tie for the strictly lowest total — survives in exactly one:
| Student | Maths | Physics | Chemistry | Total |
|---|---|---|---|---|
| Anil | 3 | 1 | 5 | 9 |
| Bela | 1 | 4 | 3 | 8 |
| Chirag | 5 | 2 | 4 | 11 |
| Dia | 2 | 5 | 1 | 8 |
| Esha | 4 | 3 | 2 | 9 |
Totals: Bela 8, Dia 8, Anil 9, Esha 9, Chirag 11. Ties are broken by Maths rank: Bela (1) above Dia (2), and Anil (3) above Esha (4). Overall order: Bela, Dia, Anil, Esha, Chirag.
| Student | Maths | Physics | Chemistry | Total |
|---|---|---|---|---|
| Anil | 3 | 1 | 5 | 9 |
| Bela | 1 | 4 | 3 | 8 |
| Chirag | 5 | 2 | 4 | 11 |
| Dia | 2 | 5 | 1 | 8 |
| Esha | 4 | 3 | 2 | 9 |
Totals: Bela 8, Dia 8, Anil 9, Esha 9, Chirag 11. Ties are broken by Maths rank: Bela (1) above Dia (2), and Anil (3) above Esha (4). Overall order: Bela, Dia, Anil, Esha, Chirag.
Question 4
Numerical answer
How many students had a better (numerically smaller) rank in Physics than in Maths?
Show answer and solution
Answer: 3
Fixed at once: Anil – Physics 1, Chemistry 5; Esha – Chemistry 2; Chirag – Maths 5. Chirag cannot also be 5th in Physics (clue 1), so (Chirag, Esha) in Physics is (2, 3) or (3, 4). The Maths topper is 3rd in Chemistry, so it is Bela or Dia (Anil, Esha, Chirag are excluded). Dia is behind Bela in Physics. Clues 1–6 still allow nine grids (e.g. with Dia topping Maths, totals come out as Anil 8 or Bela 7 — lower than Dia's), and clue 7 — Bela and Dia tie for the strictly lowest total — survives in exactly one:
| Student | Maths | Physics | Chemistry | Total |
|---|---|---|---|---|
| Anil | 3 | 1 | 5 | 9 |
| Bela | 1 | 4 | 3 | 8 |
| Chirag | 5 | 2 | 4 | 11 |
| Dia | 2 | 5 | 1 | 8 |
| Esha | 4 | 3 | 2 | 9 |
Compare Physics vs Maths: Anil 1 vs 3 ✓, Bela 4 vs 1 ✗, Chirag 2 vs 5 ✓, Dia 5 vs 2 ✗, Esha 3 vs 4 ✓. Answer: 3.
| Student | Maths | Physics | Chemistry | Total |
|---|---|---|---|---|
| Anil | 3 | 1 | 5 | 9 |
| Bela | 1 | 4 | 3 | 8 |
| Chirag | 5 | 2 | 4 | 11 |
| Dia | 2 | 5 | 1 | 8 |
| Esha | 4 | 3 | 2 | 9 |
Compare Physics vs Maths: Anil 1 vs 3 ✓, Bela 4 vs 1 ✗, Chirag 2 vs 5 ✓, Dia 5 vs 2 ✗, Esha 3 vs 4 ✓. Answer: 3.
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