Question 1: A mixture contains three types of fruit: apples, bananas, and oranges. The ratio of apples to bananas to oranges is 3:4:5. If the total number of fruits is 120, how many of each fruit are there?

Answer: {"apples":36,"bananas":48,"oranges":36}

Question 2: A cake is divided into parts in the ratio 2:3:5. If the largest part weighs 50 grams, what is the total weight of the cake?

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Question 3: A class has 30 students. The ratios of boys to girls in different groups are 2:3, 4:5, and 3:4. If the total number of students in all groups is 21, how many students are in each group?

Answer: {"group1":8,"group2":9,"group3":4}

Question 4: In a ratio 5:7:8, the sum of the parts is 120. Find the value of each part.

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Question 5: A farmer distributes 240 kg of produce among three markets in the ratio 4:3:5. How much produce does each market receive?

Answer: {"market1":48,"market2":36,"market3":60}

Question 6: A recipe calls for ingredients in the ratio 3:2:5. If the total weight of ingredients used is 100g, what is the weight of each ingredient?

Answer: {"ingredient1":15,"ingredient2":10,"ingredient3":75}

Question 7: A company splits its profits among three departments in the ratio 6:4:5. If Department A receives $1800, how much do Departments B and C receive combined?

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Question 8: Construct a triangle on the grid where the sides are in the ratio 3:4:5, with the shortest side measuring 3 units. Show all steps.

Answer: Correctly constructed 3:4:5 triangle

Question 9: A water tank is filled in such a way that the ratio of water to air in the tank is 7:3. If the tank contains 1400 liters of mixture, how many liters of water are in the tank?

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Question 10: A chain is divided into parts in the ratio 11:13:16. If the total length is 240 cm, find the length of each part.

Answer: {"part1":60,"part2":70,"part3":110}

Question 11: Identify and correct the mistake in this ratio sharing problem: 'A recipe requires ingredients in the ratio 2:3:4. If the total weight is 36 grams, each ingredient weighs 12 grams.'

Answer: The mistake is that the ratio parts sum to 9, so each part is 4 grams, not 12 grams. Correct weights are 8g, 12g, and 16g.