1. Agra is north of Erode and west of Calcutta. 2. Bombay is north of Agra and…

In a direction-sense puzzle, each statement gives a North-South relation and an East-West relation between two places. Plot all places on two independent scales -- one North-South, one East-West -- using the transitive rule (if A is north of B and B is north of C, then A is north of C, and similarly for east-west). A place is only north-and-east of a reference point when BOTH its position on the North-South scale is above the reference AND its position on the East-West scale is to the right of the reference.

1. North-South scale: Statement 1 gives Agra north of Erode; statement 4 gives Erode north of Faridabad; statement 5 gives Faridabad north of Delhi; statement 6 gives Faridabad north of Calcutta. Chaining these: Agra is above Erode, which is above Faridabad, with Delhi and Calcutta both below Faridabad.

2. East-West scale: statement 5 gives Faridabad west of Agra; statement 1 gives Agra west of Calcutta; statement 3 gives Agra west of Delhi; statement 6 gives Calcutta west of Delhi; statement 4 gives Delhi west of Erode. Chaining these: Faridabad is west of Agra, which is west of Calcutta, which is west of Delhi, which is west of Erode.

3. Faridabad has the smallest value on the East-West scale among these towns, so Agra, Calcutta, Delhi, and Erode are all east of Faridabad -- the east condition is satisfied by all of them, so the discriminator is the north condition alone.

4. Check the north condition against each numbered choice: (I) Agra sits above Faridabad on the North-South scale, so it satisfies north. (II) Calcutta sits below Faridabad (directly, from statement 6), so it fails north. (III) Erode sits above Faridabad (directly, from statement 4), so it satisfies north.

Cross-check: Statement 4 directly states Erode is north of Faridabad, and Agra is north of Erode (statement 1), hence north of Faridabad by transitivity -- both are independently confirmed north and, from the East-West chain, both are independently confirmed east. Calcutta is explicitly placed south of Faridabad in statement 6, ruling it out regardless of its East-West position.

Result: Both Agra (I) and Erode (III) must be north and east of Faridabad, while Calcutta (II) is ruled out for lying south of Faridabad -- so the correct choice is “I and III.”