1. Agra is north of Erode and west of Calcutta. 2. Bombay is north of Agra and…
2025
1. Agra is north of Erode and west of Calcutta.
2. Bombay is north of Agra and west of Federicktown.
3. Delhi is south and east of Agra
4. Erode is north of Faridabad and east of Delhi.
5. Faridabad is north of Delhi and west of Agra.
6. Calcutta is south of Faridabad and west of Delhi.
Q3. Which of the following towns must be situated both south and west of at least one other town ?
- A.
Agra only
- B.
Agra and Faridabad
- C.
Delhi and Faridabad
- D.
Delhi, Calcutta, and Faridabad
Attempted by 2 students.
Show answer & explanation
Correct answer: D
Concept: In a direction-sense puzzle, north-south and east-west are two independent axes. A town is south-and-west of another town only when both orderings hold together on that same pair of towns - south on the north-south axis and west on the east-west axis - and both must be forced by the statements, directly or by chaining statements along the same axis, never assumed.
East-west chain (west to east): statement 5 places Faridabad west of Agra; statement 1 places Agra west of Calcutta; statement 3 places Delhi east of Agra; statement 6 places Calcutta west of Delhi; statement 4 places Erode east of Delhi. Chaining these gives one fixed order from west to east: Faridabad, Agra, Calcutta, Delhi, Erode.
North-south chain (south to north): statement 3 places Delhi south of Agra; statement 5 places Faridabad north of Delhi; statement 4 places Erode north of Faridabad; statement 1 places Agra north of Erode; statement 2 places Bombay north of Agra. Chaining these gives Delhi, Faridabad, Erode, Agra, Bombay, from south to north.
Statement 6 also places Calcutta south of Faridabad. Since Faridabad already sits below Erode and Agra in the chain above, Calcutta is therefore south of Faridabad, Erode, and Agra as well - though its position relative to Delhi specifically is never fixed by any statement.
Town | West-east position | North-south position | South and west of another town? |
|---|---|---|---|
Agra | West of Calcutta, Delhi, Erode | North of Calcutta, Delhi, Erode; south of Bombay | No - west of three towns it is north of; south of Bombay but their west-east relation is never fixed |
Erode | East of the whole chain | North of Faridabad, Delhi, Calcutta | No - never west of a town it is also south of |
Delhi | West of Erode | South of Erode | Yes - south and west of Erode |
Faridabad | West of Agra, Calcutta, Delhi, Erode | South of Agra and Erode | Yes - south and west of Agra, and of Erode |
Calcutta | West of Delhi and Erode | South of Erode (via Faridabad) | Yes - south and west of Erode, even though it sits east of Agra and Faridabad |
Cross-check Calcutta independently: Calcutta is south of Faridabad (given directly), and Faridabad is south of Erode (from the chain), so Calcutta must be south of Erode by transitivity along the same axis. Combined with Calcutta being west of Delhi (given) and Delhi being west of Erode (from the chain), Calcutta is also west of Erode by the same transitivity. So Calcutta's qualification holds on its own terms against Erode, independent of its relation to Agra, where the statements actually place it to the east, not the west.
So the towns that must be south and west of at least one other town are Delhi, Calcutta, and Faridabad.