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Ratio between officers and soldiers was 3 : 31 in a city. 6 officers and 22 soldiers were killed in a…

Let the initial number of officers and soldiers be \(3x\) and \(31x\). After \(6\) officers and \(22\) soldiers were killed: \(\frac{3x - 6}{31x - 22} = \frac{1}{13}…

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Ratio between officers and soldiers was 3 : 31 in a city. 6 officers and 22 soldiers were killed in a war and ratio became 1 : 13. Initially number of officers was equal to

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Let the initial number of officers and soldiers be 3x3x and 31x31x. After 66 officers and 2222 soldiers were killed: 3x−631x−22=113  ⟹  39x−78=31x−22  ⟹  8x=56  ⟹  x=7\frac{3x - 6}{31x - 22} = \frac{1}{13} \implies 39x - 78 = 31x - 22 \implies 8x = 56 \implies x = 7. Therefore, the initial number of officers =3x=3×7=21= 3x = 3 \times 7 = \mathbf{21}.

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