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If 80% of A is 13 more than 90% of B, and the ratio of 40% of A to 60% of B is 10 : 9, then what is the value of A -B?
50
80
20
60
- Let's first analyze the given conditions:
- 80% of A is 13 more than 90% of B, expressed as: 0.8A = 0.9B + 13.
- The ratio of 40% of A to 60% of B is 10:9, expressed as: (0.4A)/(0.6B) = 10/9.
- Simplifying the second equation:
- Multiply both sides by 0.6B to get: 0.4A = 0.6B * (10/9).
- This results in: 0.4A = (2/3)B.
- From these equations, we can find A and B:
- Substitute B from the second equation into the first: 0.8A = 0.9((3/2)(0.4A)) + 13.
- Solve this to get the relation between A and B.
- Finally, solve for A-B and find the value.
- After calculating, the correct option is: Option 1: 50
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