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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Question : The average weight of a group of 20 persons is 40 kg. The average weight of another group of 40 persons is K kg. If the average weight of all the 60 persons is 60 kg, then what is the value of K?
Option 1: 80
Option 2: 60
Option 3: 40
Option 4: 70
Question : If a number A is 40% less than another number B and B is 20% more than 100, then what is the value of A?
Option 1: 58
Option 2: 84
Option 3: 72
Option 4: 66
Question : The ratio of 45% of 80% of A to 30% of 40% of B is 15 : 4. If the average of A and B is 67.5, what is the value of A – B?
Option 1: 10
Option 2: 18
Option 3: 12
Option 4: 15
Question : Find the value of 5(12 + 20 ÷ 10 × 3 – 5).
Option 2: 35
Option 3: 65
Option 4: 40
Question : Find the value of {20 of 4 + (40 – 14 + 30) – 84}.
Option 1: 55
Option 2: 50
Option 3: 52
Option 4: 44
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