Question : In a regiment, the ratio between the number of officers to soldiers was 3 : 31 before the battle. In a battle, 6 officers and 22 soldiers were killed. The ratio became 1 : 13. The number of officers in the regiment before the battle was:
Option 1: 31
Option 2: 38
Option 3: 21
Option 4: 28
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Correct Answer: 21
Solution : Before the battle: Let the number of officers be $3x$. Let the number of soldiers be $31x$. After the battle: Let the number of officers be $3x-6$. Let the number of soldiers be $31x-22$. According to the given condition, $\frac{3x-6}{31x-22}=\frac{1}{13}$ $⇒39x-78=31x-22$ $⇒8x=56$ $\therefore x=7$ So, the number of officers before the battle = 3 × 7 = 21 Hence, the correct answer is 21.
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Question : Before the battle, the ratio of tanks to planes in an army was 5 : 3. During the war, 1000 tanks were destroyed and 800 planes were destroyed. The ratio of tanks to planes became 2 : 1, what was the number of tanks after the war?
Option 1: 2000
Option 2: 1000
Option 3: 3000
Option 4: 4000
Question : The perimeter of an equilateral triangle is equal to the circumference of a circle. The ratio of their areas is: ( Use $\pi =\frac{22}{7}$)
Option 1: $22 : 21\sqrt{3}$
Option 2: $21: 22\sqrt{3}$
Option 3: $21: 22\sqrt{2}$
Option 4: $22: 21\sqrt{2}$
Question : The mode of the following data is __________. 13, 15, 31, 12, 27, 13, 27, 30, 27, 28 and 16
Option 1: 28
Option 2: 27
Option 3: 30
Option 4: 31
Question : Which of the following is the lowest ratio?
Option 1: 8 : 19
Option 2: 15 : 38
Option 3: 17 : 38
Option 4: 13 : 19
Question : The value of $1 \frac{3}{4}+1 \frac{5}{7} \div 2 \frac{3}{7} \times 2 \frac{3}{7}=$?
Option 1: $1 \frac{11}{28}$
Option 2: $2 \frac{13}{28}$
Option 3: $3 \frac{13}{28}$
Option 4: $4 \frac{23}{28}$
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