Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different exchange values. Crown's currency exchange rate with Zentars = 0.5, i.e., 1 Crown is worth 0.5 Zentars.

Three travelers, Jano, Kira, and Lian set out from Zerathania visiting exactly two of the countries. Each country is visited by exactly two travelers. Each traveler has a unique Flight Cost, which represents the total cost of airfare in traveling to both the countries and back to Zerathania. The Flight Cost of Jano was 4000 Zentars, while that of the other two travelers were 5000 and 6000 Zentars, not necessarily in that order. When visiting a country, a traveler spent either 1000, 2000 or 3000 in the country's local currency. Each traveler had different spends (in the country's local currency) in the two countries he/she visited. Across all the visits, there were exactly two spends of 1000 and exactly one spend of 3000 (in the country's local currency).

The total “Travel Cost” for a traveler is the sum of his/her Flight Cost and the money spent in the countries visited.

The citizens of the four countries with knowledge of these travels made a few observations, with spends measured in their respective local currencies:

i. Aurevia citizen: Jano and Kira visited our country, and their Travel Costs were 3500 and 8000, respectively.

ii. Brelosia citizen: Kira and Lian visited our country, spending 2000 and 3000, respectively. Kira's Travel Cost was 4000.

iii. Cyrenia citizen: Lian visited our country and her Travel Cost was 36000.

Which of the following statements is NOT true about money spent in the local currency?

The correct option is: Jano spent 2000 in Aurevia.

Here is the step-by-step breakdown of the logical puzzle to determine the exchange rates and spends for each traveler.

1. Identify the Countries, Currencies, and Travelers:
- Countries & Currencies:
• Aurevia (A) — Aurels
• Brelosia (B) — Brins
��� Cyrenia (C) — Crowns (Exchange rate with Zentars: 1 Crown = 0.5 Zentars)
• Zerathania (Z) — Zentars (Starting country)
- Travelers: Jano (J), Kira (K), Lian (L)

2. Analyze the Visits:
Since each traveler visits exactly two countries and each country is visited by exactly two travelers, we can determine the visits based on the observations:
• Jano and Kira visited Aurevia (A).
• Kira and Lian visited Brelosia (B).
• Lian (and therefore Jano, to make exactly 2 visits per country) visited Cyrenia (C).
Thus, the itineraries are:
• Jano: Aurevia (A) and Cyrenia (C)
• Kira: Aurevia (A) and Brelosia (B)
• Lian: Brelosia (B) and Cyrenia (C)

3. Analyze the Spends:
Let $e_A$, $e_B$, and $e_C$ be the exchange rates of Aurels, Brins, and Crowns to Zentars, respectively. We are given:

$e_C=0.5$

From the Brelosia citizen's observation, Kira and Lian spent 2000 and 3000 respectively in Brelosia. Thus:

$S_{KB}=2000$
$S_{LB}=3000$

Since across all visits there were exactly two spends of 1000, one spend of 3000, and the remaining must be 2000, the set of all six spends is $\{1000,1000,2000,2000,2000,3000\}$.
We are told that each traveler had different spends in the two countries they visited.
• For Kira: $S_{KA}\ne S_{KB}\Rightarrow S_{KA}\ne 2000$.
Since the only available values are 1000 and 2000 (as the single 3000 is spent by Lian in Brelosia), we must have:

$S_{KA}=1000$

• For Lian: $S_{LC}\ne S_{LB}\Rightarrow S_{LC}\ne 3000$. Since 3000 is already taken, $S_{LC}$ must be 2000.
• For Jano: The remaining spends are $\{S_{JA},S_{JC}\}=\{1000,2000\}$.

4. Solve for the Exchange Rates and Flight Costs:
Let us write the equations for Travel Costs (TC) in terms of Zentars:
- From the Aurevia citizen: Jano's Travel Cost is 3500 Aurels, and Kira's is 8000 Aurels.
• Jano: $T{C}_J=3500\cdot e_A$
• Kira: $T{C}_K=8000\cdot e_A$ - From the Brelosia citizen: Kira's Travel Cost is 4000 Brins.
• Kira: $T{C}_K=4000\cdot e_B$
Equating Kira's Travel Cost:

$8000\cdot e_A=4000\cdot e_B\Rightarrow e_B=2e_A$

We also know that Kira's total Travel Cost is:

$T{C}_K=F{C}_K+S_{KA}\cdot e_A+S_{KB}\cdot e_B$

Substitute the values $S_{KA}=1000$, $S_{KB}=2000$, and $e_B=2e_A$ into Kira's Travel Cost equation:

$8000\cdot e_A=F{C}_K+1000\cdot e_A+2000\cdot \left(2e_A\right)$
$8000\cdot e_A=F{C}_K+5000\cdot e_A$
$F{C}_K=3000\cdot e_A$

Since the Flight Costs of Kira and Lian are 5000 and 6000 Zentars (in some order):
• If $F{C}_K=5000$, then $e_A=\frac{5}{3}$, $e_B=\frac{10}{3}$, and $F{C}_L=6000$.
Let's check Lian's Travel Cost from the Cyrenia citizen: Lian's Travel Cost is 36000 Crowns.
In Zentars, Lian's Travel Cost is $36000\cdot 0.5=18000$ Zentars.
Lian's Travel Cost equation:
$T{C}_L=F{C}_L+S_{LB}\cdot e_B+S_{LC}\cdot e_C$
Substitute the values:
$18000=6000+3000\cdot \left(\frac{10}{3}\right)+2000\cdot 0.5=6000+10000+1000=17000$ (Contradiction: $18000\ne 17000$).
• If $F{C}_K=6000$, then $e_A=2$, $e_B=4$, and $F{C}_L=5000$.
Substitute these values into Lian's equation:
$18000=5000+3000\cdot 4+2000\cdot 0.5=5000+12000+1000=18000$ (Consistent!).
Thus, the correct parameters are:
• $e_A=2$
• $e_B=4$

5. Determine Jano's Spends:
Jano's Flight Cost is $F{C}_J=4000$ Zentars.
Jano's Travel Cost equation:

$T{C}_J=F{C}_J+S_{JA}\cdot e_A+S_{JC}\cdot e_C$

Substitute Jano's total cost in Zentars, $T{C}_J=3500\cdot e_A=7000$ Zentars:

$7000=4000+S_{JA}\cdot 2+S_{JC}\cdot 0.5$
$2S_{JA}+0.5S_{JC}=3000$

Since $\{S_{JA},S_{JC}\}=\{1000,2000\}$, let's test the two possibilities:
• If $S_{JA}=1000$ and $S_{JC}=2000$:
$2\left(1000\right)+0.5\left(2000\right)=2000+1000=3000$ (Works).
• If $S_{JA}=2000$ and $S_{JC}=1000$:
$2\left(2000\right)+0.5\left(1000\right)=4000+500=4500\ne 3000$ (Fails).

Therefore, Jano spent 1000 in Aurevia and 2000 in Cyrenia.

Conclusion:
The statement "Jano spent 2000 in Aurevia" is NOT true, making it the correct option to choose.