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
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Correct Answer: 15
Solution : The ratio of 45% of 80% of A to 30% of 40% of B is 15 : 4. The average of A and B is 67.5. According to the question, $\frac{\frac{45}{100}\times\frac{80}{100}\times \text{A}}{\frac{30}{100}\times\frac{40}{100}\times \text{B}} = \frac{15}{4}$ ⇒ $\frac{3\text{A}}{\text{B}} = \frac{15}{4}$ ⇒ $\frac{\text{A}}{\text{B}} = \frac{5}{4}$ So, take A = 5x and B = 4x Sum of A and B = 67.5 × 2 = 135 ⇒ 5x + 4x = 135 ⇒ 9x = 135 ⇒ x = 15 $\therefore$ A – B = 5x – 4x = x = 15 Hence, the correct answer is 15.
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Question : What is the value of $\frac{6}{13}[\frac{29}{12}+\frac{4}{18}(\frac{16}{12}+\frac{18}{9})–\frac{46}{15} \div \frac{23}{45}]$?
Option 1: $\frac{–312}{137}$
Option 2: $\frac{–307}{234}$
Option 3: $\frac{–294}{117}$
Option 4: $\frac{–207}{119}$
Question : The value of $12 ÷ (\frac{1}{2})+\{(35 ÷ 7)\text{ of }40\}+20-15\text{ of }10$ is:
Option 1: 88
Option 2: 94
Option 3: 99
Option 4: 80
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
Question : Find the value of p, when p = (5 ÷ 6) of 54 – 40 ÷ 10 – 41 – 22
Option 1: –11
Option 2: –22
Option 3: –18
Option 4: –23
Question : The value of 3 × [{(11 – 3) ÷ ($\frac{1}{2}$) of 8} + 15 ÷ 3] is:
Option 1: 15
Option 2: 19
Option 3: 21
Option 4: 30
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