Mindyard | 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. One Brin is equivalent to how many Crowns? 4, 0.5, 8, 0.125

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.

One Brin is equivalent to how many Crowns?

Options

0.5

0.125

Correct Answer :

Option C

Solution :

The correct option is 8.

Detailed Step-by-Step Derivation:

1. Travelers and Country Visits:
From the citizen observations, the travelers visited the following countries:
- Kira visited Aurevia and Brelosia.
- Lian visited Brelosia and Cyrenia.
- Jano visited Aurevia and Cyrenia.

2. Currency Exchange Values:
Let the values of Aurels, Brins, and Crowns in terms of Zentars be $e_{A}$ , $e_{B}$ , and $e_{C}$ , respectively.
We are given that 1 Crown = 0.5 Zentars, which means:

$e_{C} = 0.5$

3. Analysing Kira's Travel Cost:
- In Brelosia (measured in Brins), Kira's Travel Cost was 4000. Thus, Kira's Travel Cost in Zentars is $4000 \times e_{B}$ .
- In Aurevia (measured in Aurels), Kira's Travel Cost was 8000. Thus, Kira's Travel Cost in Zentars is $8000 \times e_{A}$ .
- Equating the two values in Zentars:

$8000 \times e_{A} = 4000 \times e_{B} implies e_{B} = 2 \times e_{A}$

4. Using Kira's Spends:
- From Brelosia's citizen, Kira spent 2000 Brins in Brelosia.
- Since spends must be different in the two countries visited, and 3000 is already spent by Lian in Brelosia, Kira's spend in Aurevia must be 1000 Aurels.
- Kira's Travel Cost in Zentars is:

$F_{Kira} + 1000 \times e_{A} + 2000 \times e_{B} = 4000 \times e_{B}$

Substituting

e_{A} = 0.5 \times e_{B}

$FKira + 500 \times e_{B} + 2000 \times e_{B} = 4000 \times e_{B} implies FKira = 1500 \times e_{B}$

5. Evaluating the Flight Cost Scenarios:
Kira's Flight Cost must be either 5000 or 6000 Zentars:
- If $FKira = 6000$ , then:

$1500 \times e_{B} = 6000 implies e_{B} = 4$

This yields Lian's Flight Cost as

FLian = 5000

Zentars. Let's verify this using Lian's Travel Cost in Cyrenia:
- Lian's Travel Cost was 36000 Crowns, which equals

36000 \times 0.5 = 18000

Zentars.
- Lian's spends were 3000 Brins in Brelosia and

S_{Lian, Cyrenia}

in Cyrenia:

$5000 + 3000 \times 4 + S_{Lian, Cyrenia} \times 0.5 = 18000$

$17000 + 0.5 \times S_{Lian, Cyrenia} = 18000 implies S_{Lian, Cyrenia} = 2000$

This is a valid spend value, confirming that the exchange rate of Brelosia's currency is

e_{B} = 4

Zentars.

6. Determining the Brin to Crown Exchange Rate:
Since 1 Brin = 4 Zentars and 1 Crown = 0.5 Zentars, the value of 1 Brin in Crowns is:

$\frac{4 \text{ Zentars}}{0.5 \text{ Zentars/Crown}} = 8 \text{ Crowns}$

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