Question : 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?
Option 1: 50
Option 2: 80
Option 3: 20
Option 4: 60
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Correct Answer: 20
Solution : From the first condition, $0.8A = 0.9B + 13$ ___(1) From the second condition, $\frac{0.4A}{0.6B} = \frac{10}{9} \Rightarrow 0.4A = \frac{10}{9} \times 0.6B$ ___(2) From equation (2), we can express A in terms of B: $A = \frac{10}{9} \times \frac{0.6B}{0.4} = \frac{5}{3}B$ ___(3) Substitute equation (3) into equation (1): $0.8 \times \frac{5}{3}B = 0.9B + 13 $ $\Rightarrow 13B = 390$ $\Rightarrow B =30$ Substitute B into equation (3) to find A, $A = \frac{5}{3} \times 30= 50$ Therefore, the value of A - B is: $A - B = 50 - 30 = 20$ Hence, the correct answer is 20.
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