Question 24

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

Solution

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 = 78-22

8x = 56

x = 7

number of officers in the regiment before battle was = 3x = 3$$\times$$7 = 21

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