Comprehension
There are 6 refineries, 7 depots and 9 districts. The refineries are BB, BC, BD, BE, BF and BG. The depots are AA, AB, AC, AD, AE, AF and AG. The districts are AAA, AAB, AAC, AAD, AAE, AAF, AAG, AAH, and AAI. Table A gives the cost of transporting one unit from refinery to depot. Table B gives the cost of transporting one unit from depot to a district.
TABLE A
| BB | BC | BD | BE | BF | BG | |
|---|---|---|---|---|---|---|
| AA | 928.2 | 537.2 | 567.8 | 589.9 | 589.9 | 800.1 |
| AB | 311.1 | 596.7 | 885.7 | 759.9 | 759.9 | 793.9 |
| AC | 451.1 | 0 | 320.1 | 780.1 | 720.7 | 1000.1 |
| AD | 371.1 | 150.1 | 350.1 | 750.1 | 650.4 | 980.1 |
| AE | 1137.3 | 314.5 | 0 | 1157.7 | 1157.7 | 1023.4 |
| AF | 617.1 | 516.8 | 756.5 | 1065.9 | 1065.9 | 406.3 |
| AG | 644.3 | 299.2 | 537.2 | 1093.1 | 1093.1 | 623.9 |
TABLE B
| AA | AB | AC | AD | AE | AF | AG | |
|---|---|---|---|---|---|---|---|
| AAA | 562.7 | 843.2 | 314.5 | 889.1 | 0 | 754.8 | 537.2 |
| AAB | 532.7 | 803.2 | 284.5 | 790.5 | 95.2 | 659.6 | 442 |
| AAC | 500.7 | 780.2 | 0 | 457.3 | 205.7 | 549.1 | 331.5 |
| AAD | 232.9 | 362.1 | 286.2 | 275.4 | 523.6 | 525.3 | 673.2 |
| AAE | 345.1 | 268.6 | 316.2 | 163.2 | 555.9 | 413.1 | 227.8 |
| AAF | 450.1 | 644.3 | 346.2 | 372.3 | 933.3 | 402.9 | 379.1 |
| AAG | 654.5 | 0 | 596.7 | 222.7 | 885.7 | 387.6 | 348.5 |
| AAH | 804.1 | 149.6 | 627.2 | 360.4 | 1035.3 | 537.2 | 498.1 |
| AAI | 646 | 255 | 433.5 | 137.7 | 698.7 | 112.2 | 161.5 |
Question: 1
What is the least cost of sending one unit from any refinery to any district?
What is the least cost of sending one unit from any refinery to any district?
Show Hint
To find the least cost, check the individual transportation costs from refinery to district and pick the minimum value.
Updated On: Jul 30, 2026
- 95.2
- 0
- 205.7
- 284.5
Show Solution
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The Correct Option is B
Solution and Explanation
From Table A and Table B, the cost of sending one unit from refinery to district is given. The minimum cost is 0, which occurs for sending from refinery AC to district AAD.
Thus, the least cost is 0.
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Question: 2
What is the least cost of sending one unit from any refinery to the district AAB?
What is the least cost of sending one unit from any refinery to the district AAB?
Show Hint
For each refinery, add the refinery-to-depot cost (Table A) and the depot-to-AAB cost (Table B, row AAB) for every depot, take the cheapest route per refinery, then the smallest overall. Watch for the depots AC and AE, which have very low costs to AAB.
Updated On: Nov 4, 2026
- 0
- 95.2
- 284.5
- None of these
Show Solution
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The Correct Option is B
Solution and Explanation
Step 1: Set up the route cost:
A route from a refinery to AAB goes through one depot. Its cost is the Table A cost (depot, refinery) plus the Table B cost (AAB, depot). The AAB row of Table B reads AA 532.7, AB 803.2, AC 284.5, AD 790.5, AE 95.2, AF 659.6, AG 442.
Step 2: Cheapest route for the refineries that matter:
BD via AE: 0 + 95.2 = 95.2 (Table A cost from BD to AE is 0). BC via AC: 0 + 284.5 = 284.5 (Table A cost from BC to AC is 0). BB: cheapest is via AC, 451.1 + 284.5 = 735.6. BF: via AC, 720.7 + 284.5 = 1005.2. BG: cheapest is via AF or AG, 406.3 + 659.6 = 1065.9 via AF, or 623.9 + 442 = 1065.9 via AG, well above 1000. BE: via AC, 780.1 + 284.5 = 1064.6.
Step 3: Compare:
The two cheapest routes are BD, AE, AAB with total 95.2 and BC, AC, AAB with total 284.5. Every other refinery costs more than 700. The least cost is 95.2.
Final Answer:
The correct option is (2): 95.2
A route from a refinery to AAB goes through one depot. Its cost is the Table A cost (depot, refinery) plus the Table B cost (AAB, depot). The AAB row of Table B reads AA 532.7, AB 803.2, AC 284.5, AD 790.5, AE 95.2, AF 659.6, AG 442.
Step 2: Cheapest route for the refineries that matter:
BD via AE: 0 + 95.2 = 95.2 (Table A cost from BD to AE is 0). BC via AC: 0 + 284.5 = 284.5 (Table A cost from BC to AC is 0). BB: cheapest is via AC, 451.1 + 284.5 = 735.6. BF: via AC, 720.7 + 284.5 = 1005.2. BG: cheapest is via AF or AG, 406.3 + 659.6 = 1065.9 via AF, or 623.9 + 442 = 1065.9 via AG, well above 1000. BE: via AC, 780.1 + 284.5 = 1064.6.
Step 3: Compare:
The two cheapest routes are BD, AE, AAB with total 95.2 and BC, AC, AAB with total 284.5. Every other refinery costs more than 700. The least cost is 95.2.
Final Answer:
The correct option is (2): 95.2
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Question: 3
What is the least cost of sending petrol from refinery BB to district AAA?
What is the least cost of sending petrol from refinery BB to district AAA?
Show Hint
Add the BB-to-depot cost (Table A, column BB) and the depot-to-AAA cost (Table B, row AAA) for each of the seven depots and take the smallest total.
Updated On: Nov 4, 2026
- 765.6
- 1137.3
- 1154.3
- None of these
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Write the route cost:
The cost via depot d is the Table A cost from BB to d plus the Table B cost from d to AAA. The AAA row of Table B reads AA 562.7, AB 843.2, AC 314.5, AD 889.1, AE 0, AF 754.8, AG 537.2.
Step 2: Compute for each depot:
AA: 928.2 + 562.7 = 1490.9. AB: 311.8 + 843.2 = 1155.0. AC: 451.1 + 314.5 = 765.6. AD: 371.1 + 889.1 = 1260.2. AE: 1137.3 + 0 = 1137.3. AF: 617.1 + 754.8 = 1371.9. AG: 644.3 + 537.2 = 1181.5.
Step 3: Take the minimum:
The least cost is 765.6, by sending BB to AC and then AC to AAA. The other listed values (1137.3 via AE) are costlier routes.
Final Answer:
The correct option is (1): 765.6
The cost via depot d is the Table A cost from BB to d plus the Table B cost from d to AAA. The AAA row of Table B reads AA 562.7, AB 843.2, AC 314.5, AD 889.1, AE 0, AF 754.8, AG 537.2.
Step 2: Compute for each depot:
AA: 928.2 + 562.7 = 1490.9. AB: 311.8 + 843.2 = 1155.0. AC: 451.1 + 314.5 = 765.6. AD: 371.1 + 889.1 = 1260.2. AE: 1137.3 + 0 = 1137.3. AF: 617.1 + 754.8 = 1371.9. AG: 644.3 + 537.2 = 1181.5.
Step 3: Take the minimum:
The least cost is 765.6, by sending BB to AC and then AC to AAA. The other listed values (1137.3 via AE) are costlier routes.
Final Answer:
The correct option is (1): 765.6
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Question: 4
How many possible ways are there for sending petrol from any refinery to any district?
How many possible ways are there for sending petrol from any refinery to any district?
Show Hint
Multiply the number of refineries by the number of districts to calculate the possible transportation ways.
Updated On: Jul 30, 2026
- 63
- 42
- 54
- 378
Show Solution
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The Correct Option is D
Solution and Explanation
There are 6 refineries and 9 districts, so the total number of ways to send petrol from any refinery to any district is \( 6 \times 9 = 54 \). Thus, the Correct Answer is 378.
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Question: 5
The largest cost of sending petrol from any refinery to any district is:
The largest cost of sending petrol from any refinery to any district is:
Show Hint
Look for the highest cost value in the table to identify the largest transportation cost.
Updated On: Aug 4, 2025
- 2172.6
- 2193.0
- 2091.0
- None of these
Show Solution
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The Correct Option is B
Solution and Explanation
The largest cost of sending petrol from any refinery to any district is 2193.0, which is from refinery BE to district AAG as shown in the tables.
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Question: 6
What is the least cost of sending one unit from refinery BB to any district?
What is the least cost of sending one unit from refinery BB to any district?
Show Hint
Find the cheapest first leg from BB to a depot, then see whether that depot has a zero-cost link to some district. Compare with the other district costs.
Updated On: Nov 4, 2026
- 284.5
- 311.1
- 451.1
- None of these
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Costs from BB to each depot (Table A, column BB):
AA 928.2, AB 311.1, AC 451.1, AD 371.1, AE 1137.3, AF 617.1, AG 644.3. The cheapest first leg is 311.1, to depot AB.
Step 2: Lower bound:
Table B costs are not negative, so every route from BB costs at least 311.1.
Step 3: A route that reaches the bound:
In Table B the cost from depot AB to district AAG is 0, so BB to AB to AAG costs 311.1 + 0 = 311.1.
Step 4: Check the other districts:
Cheapest BB cost per district: AAA 765.6 (via AC), AAB 735.6 (AC), AAC 451.1 (AC), AAD 646.5 (AD), AAE 534.3 (AD), AAF 743.4 (AD), AAG 311.1 (AB), AAH 461.4 (AB), AAI 508.8 (AD). The minimum is 311.1.
Final Answer:
The correct option is (2): 311.1
AA 928.2, AB 311.1, AC 451.1, AD 371.1, AE 1137.3, AF 617.1, AG 644.3. The cheapest first leg is 311.1, to depot AB.
Step 2: Lower bound:
Table B costs are not negative, so every route from BB costs at least 311.1.
Step 3: A route that reaches the bound:
In Table B the cost from depot AB to district AAG is 0, so BB to AB to AAG costs 311.1 + 0 = 311.1.
Step 4: Check the other districts:
Cheapest BB cost per district: AAA 765.6 (via AC), AAB 735.6 (AC), AAC 451.1 (AC), AAD 646.5 (AD), AAE 534.3 (AD), AAF 743.4 (AD), AAG 311.1 (AB), AAH 461.4 (AB), AAI 508.8 (AD). The minimum is 311.1.
Final Answer:
The correct option is (2): 311.1
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