Ina regiment the ratio between the numberofofficers to soldiers was 3 : 31 before battle. In a battle 6 officers and 22 soldiers werekilled and theratio 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
$$\frac{3x-6}{31x-22}$$= $$\frac{1}{13}$$
13(3x-6) = 31x -22
39x - 78 = 31x -22
8x = 78-22Â
8x = 56
x = 7
 number of officers in the regiment before battle was = 3x = 3$$\times$$7 = 21
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