Ina regiment the ratio between the number of officers to soldiers was 3 : 31 before battle. In a battle 6 officers and 22 soldiers were killed and the ratio became 1 : 13, the number of officers in the regiment before battle was
no of officers : no of soldiers = 3:31 no of officers = 3x no of soldiers = 31x In a battle 6 officers and 22 soldiers were killed new no of officers = 3x-6 new no of soldiers = 31x -22 new ratio 1:13 (3x – 6) / (31x – 22) = 1/13 13(3x-6) = 31x -22 39x - 78 = 31x -22 8x = 78-22 8x = 56 x = 7 number of officers in the regiment before battle was = 3x = 3 × 7 = 21
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