CAT 2025 Slot 3 · DILR · Question 5

CAT 2025 Slot 3 previous year question on Quant Based Puzzles and Optimisation, with the answer and a step-by-step solution.

Quant Based Puzzles and OptimisationLOGICAL REASONING - High LevelType in the answer (TITA)Hard

Set 2: Travellers and Exchange Rates — this question belongs to a set. Read the full set with all 5 questions →

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.

What is the sum of Travel Costs for all travelers in Zentars?

Answer & solution

Answer: 41000

Who went where: three travellers make 6 visits, and each country gets exactly 2, so the three countries visited are Aurevia, Brelosia and Cyrenia. Aurevia: Jano, Kira. Brelosia: Kira, Lian. Jano's second country must be Cyrenia, so Cyrenia: Jano, Lian.

Spends (local currency): Lian spent 3000 in Brelosia (the only 3000) and Kira 2000 there. Kira's two spends differ, so Kira spent 1000 in Aurevia. That leaves one more 1000 and two more 2000s among Jano–Aurevia, Jano–Cyrenia and Lian–Cyrenia. Jano's two spends must differ, so Jano has one 1000 and one 2000, and Lian spent 2000 in Cyrenia.

Exchange rates: let 1 Aurel = a Zentars and 1 Brin = b Zentars; 1 Crown = 0.5 Zentars.

Kira's Travel Cost is 8000 Aurels and also 4000 Brins, so 8000a = 4000b, giving b = 2a. In Zentars: Flight(K) + 1000a + 2000b = 8000a, so Flight(K) = 8000a − 1000a − 4000a = 3000a.

Lian's Travel Cost is 36000 Crowns = 18000 Zentars: Flight(L) + 3000b + 2000 × 0.5 = 18000, so Flight(L) = 17000 − 6000a.

Flight(K) and Flight(L) are 5000 and 6000. Flight(K) = 3000a gives a = 5/3 or 2; a = 5/3 makes Flight(L) = 7000 (not allowed), so a = 2, b = 4, Flight(K) = 6000, Flight(L) = 5000.

Jano's Travel Cost is 3500 Aurels = 7000 Zentars, so his spends total 7000 − 4000 = 3000 Zentars. Aurevia 1000 (= 2000 Z) + Cyrenia 2000 (= 1000 Z) = 3000 Z works; the reverse (4000 Z + 500 Z) does not.

Travel Costs in Zentars: Jano 7000, Kira 8000 × 2 = 16000, Lian 18000. Sum = 41000.

Shortcut: Kira's cost in two currencies gives b = 2a at once; the flight-cost options then force a = 2.

Hence, the answer is 41000.

CAT 2025 Slot 3 · DILR · Question 5

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