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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