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In a city X, there are 240 users who use three different types of vehicles, i.e. bike, car, and truck. The number of users of all the three vehicles is 2.5% of the total number of users. The number of users of both car and truck is 36 more than the users of only bikes. The number of users of both car and bike is equal to the number of users of both truck and bike. The number of users of both car and bike is half the number of users of only bikes, and the number of users of only truck is 10 less than the number of users of only bikes. The number of users of only bike is 34. Find the ratio of the number of users of only car to only truck.

1. 2: 3
2. 3: 1
3. 3: 2
4. 4: 1

Correct answer: 3: 1

Solution

Using only bike = 34, the overlap of car and bike is half of that, so 17. The overlap of truck and bike is also 17, and only truck = 24. Using the total 240 and the condition on all three vehicles, the only car count comes out to 72, giving the ratio 72:24 = 3:1.

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