Question

Five women decided to go shopping at a mall. They arrived at the designated meeting place in the following order: 1. Archana, 2. Chellamma, 3. Dhenuka, 4. Helen, and 5. Shahnaz. Each woman spent at least Rs. 1000. Below are some additional facts about how much they spent during their shopping spree. The woman who spent Rs. 1193 is which of the following:

• A. Dhenuka
• B. Chellamma
• C. Helen
• D. Archana
• E. Shahnaz

Hint:

In such puzzles, systematically test possibilities using the given constraints to narrow down assignments.

Answer 1

The Correct Option is A

Step 1: Listing Known Facts:
Arrival order: 1. Archana, 2. Chellamma, 3. Dhenuka, 4. Helen, 5. Shahnaz.
Given amounts in clues: Rs. 2234, Rs. 1193, Rs. 1340, Rs. 2517.
Clue (vi): Shahnaz spent largest, Chellamma spent smallest.
Clue (iii): One woman spent Rs. 1378 more than Chellamma.
Let Chellamma's amount = \(C\). Then \(C + 1378\) is another amount.
The amounts are five numbers: \(C\), \(C+1378\), and the four given numbers 1193, 1340, 2234, 2517 but one of these given numbers is actually \(C+1378\).

Step 2: Determining Chellamma's Amount:
Try each given number as \(C+1378\):
If \(C+1378 = 1193\) → \(C = -185\) (invalid)
If \(C+1378 = 1340\) → \(C = -38\) (invalid)
If \(C+1378 = 2234\) → \(C = 856\) (invalid, as each spent at least Rs. 1000)
If \(C+1378 = 2517\) → \(C = 1139\) (valid)
So, \(C = 1139\) (Chellamma's amount) and \(C+1378 = 2517\) is another amount.
Thus, Shahnaz (largest) = Rs. 2517.

Step 3: Identifying Rs. 1193:
Remaining amounts: 1193, 1340, 2234.
Clue (i): Woman who spent 2234 arrived before woman who spent 1193.
Clue (ii): Rs. 1340 was spent by someone not Dhenuka.
Clue (iv): Rs. 2517 was not spent by Archana.
Clue (v): Helen spent more than Dhenuka.
Order of arrival: Archana (1), Chellamma (2, spent 1139), Dhenuka (3), Helen (4), Shahnaz (5, spent 2517).
Since Chellamma is smallest (1139), all others > 1139.
Remaining amounts for Archana, Dhenuka, Helen: 1193, 1340, 2234.
Helen > Dhenuka, so Dhenuka cannot have 2234.
Also, 2234 arrived before 1193 (clue i). So if 2234 is with Archana (pos 1) and 1193 with Dhenuka (pos 3) or Helen (pos 4), that works.
If 2234 with Dhenuka (pos 3), then 1193 must be after, so with Helen (pos 4) — possible.
If 2234 with Helen (pos 4), then 1193 must be after, but no one after Helen except Shahnaz (2517), so impossible.
Thus, 2234 must be with Archana (pos 1) or Dhenuka (pos 3).
But 2234 arrived before 1193:
- If Archana (pos 1) has 2234, then 1193 can be with Dhenuka (pos 3) or Helen (pos 4).
- If Dhenuka (pos 3) has 2234, then 1193 must be with Helen (pos 4).
Also, clue (ii): 1340 not Dhenuka. So Dhenuka cannot have 1340.
Now check Helen > Dhenuka:
Case 1: Dhenuka = 1193, Helen = 1340 → 1340 > 1193 ✓, then Archana = 2234.
Case 2: Dhenuka = 1193, Helen = 2234 → 2234 > 1193 ✓, then Archana = 1340. But 1340 not Dhenuka ✓.
Case 3: Dhenuka = 1340? Not allowed (clue ii). So Dhenuka ≠ 1340.
Case 4: Dhenuka = 2234, then Helen must be >2234, but only 2517 is larger (Shahnaz), so Helen cannot be >2234. So Dhenuka ≠ 2234.
Thus Dhenuka must be 1193.

Step 4: Final Answer:
The woman who spent Rs. 1193 is Dhenuka.