Correct option is C
Given:
- Five girls: Henna, Agatha, Dipti, Lata, Shabnam
- Condition 1: Henna is to the left of Agatha
- Condition 2: Between Agatha and Dipti, there are 3 places
- Condition 3: Shabnam has both Lata and Dipti as neighbours
Solution:
Step 1: Use Condition 2
Between Agatha and Dipti there are 3 places
→ So they must be at positions 1 & 5 or 2 & 4.
But with 5 girls total, only position pairs (1,5) can have 3 places between them.
So:
- Agatha and Dipti are at positions 1 and 5 (in some order)
Now consider the directional condition:
Henna is to the left of Agatha
So if Agatha is at position 5, Henna can be anywhere from 1–4
If Agatha is at 1, then Henna can’t be to the left, so that’s invalid.
=>Agatha = 5, Dipti = 1
Step 2: Place Henna
Henna is to the left of Agatha (5)
So Henna can be at position 1, 2, 3, or 4
But Dipti is already at position 1
So, Henna = 2, 3, or 4
We'll revisit this after placing others.
Step 3: Use Condition 3
Shabnam has both Lata and Dipti as neighbours
Dipti is at position 1, so for her to be a neighbour of Shabnam, Shabnam must be at position 2.
Then the only way Shabnam can have both Lata and Dipti as neighbours is:
- Dipti – Shabnam – Lata = positions 1–2–3
So:
- Dipti = 1
- Shabnam = 2
- Lata = 3
Step 4: Who’s left?
We’ve used:
- Dipti (1)
- Shabnam (2)
- Lata (3)
- Agatha (5)
So, position 4 must be Henna
→ Henna = 4
→ Agatha = 5
Final Order:
Dipti, Shabnam, Lata, Henna, Agatha
Now check the options:
A. Lata is to the right of Agatha → False (Lata is at 3, Agatha at 5)
B. Henna is at the extreme left → False (Henna is at 4)
C. There are exactly two places between Henna & Dipti
- Dipti = 1, Henna = 4 → positions 2 & 3 between them → True
D. There is exactly one place between Shabnam & Agatha
- Shabnam = 2, Agatha = 5 → 2 places: 3 and 4 between → False
Correct Option: (C) There are exactly two places between Henna & Dipti
