Study the following information carefully and answer the questions given below:

Six persons — A, B, C, D, E and F — have different heights, but not necessarily in the same order. More than two persons are shorter than E. C is two persons taller than E. Height of tallest person is 182cm. Height of A is 156cm. F is shorter than A. Only two persons are shorter than D. B is taller than A but shorter than C.

If the height of D is 20cm less than the height of C then what is the possible height of E?

To find the possible height of E, we must first determine the relative heights of all six individuals: A, B, C, D, E, and F. Let us represent their heights using a ranking system from 1 (tallest) to 6 (shortest).

1. Analyze the clues:
- Total number of persons = 6.
- "Only two persons are shorter than D." This means there are exactly two positions below D. So, D must be in the 4th position.
_ > _ > _ > D > _ > _
- "More than two persons are shorter than E." This means E is taller than at least 3 people. Thus, E cannot be in positions 4, 5, or 6. E must be in position 1, 2, or 3.
- "C is two persons taller than E." This means C is placed two positions ahead of E (i.e., C > [someone] > E). Since C must be taller than E, E cannot be in position 1 or 2. If E were in position 3, C would be in position 1. Since E must be in position 1, 2, or 3, the only logical position for E is 3, which forces C to be in position 1.
Let us place C and E:
C (1st) > _ (2nd) > E (3rd) > D (4th) > _ (5th) > _ (6th)
- "B is taller than A but shorter than C." Since C is in the 1st position, B and A must occupy some of the remaining positions. We are told B > A.
- "F is shorter than A." This means A > F.
- Combining these relations, we have B > A > F.
Looking at our remaining empty slots (2nd, 5th, and 6th), B must be placed in the 2nd slot, A in the 5th slot, and F in the 6th slot to maintain the order B > E > D > A > F (since E and D are already fixed at 3rd and 4th).
Let us verify the final arrangement:
C (1st) > B (2nd) > E (3rd) > D (4th) > A (5th) > F (6th)

2. Analyze the heights:
- Height of the tallest person (C) = 182 cm.
- Height of A (5th) = 156 cm.
- The problem states: "If the height of D is 20cm less than the height of C..."
Therefore, the height of D = Height of C - 20 cm = 182 cm - 20 cm = 162 cm.

3. Determine the possible height of E:
From our ordering, E is taller than D but shorter than B (who is shorter than C).
So, the height of E must lie between the height of D and the height of C.
Height of D < Height of E < Height of C
162 cm < Height of E < 182 cm
Looking at the given options:
- 157 cm (not in range)
- 158 cm (not in range)
- 160 cm (not in range)
- 170 cm (within the range of 162 cm to 182 cm)
- 189 cm (not in range)

Thus, the only possible height for E among the options is 170 cm.