In a regiment the ratio between the number of officers to soldiers was 3 : 31 before. In a battle 6 officers and 22 soldiers were killed and the ratio become 1 : 13, the number of officers in the regiment before battle was?

Question: In a regiment the ratio between the number of officers to soldiers was 3 : 31 before. In a battle 6 officers and 22 soldiers were killed and the ratio become 1 : 13, the number of officers in the regiment before battle was?

Solution:
Let, the number of officers and soldiers = 3x, 31x

ATQ,
(3x - 6)/(31x - 22) = 1/13
⇒ 39x - 78 = 31x - 22
⇒ 39x - 31x = - 22 + 78
⇒ 8x = 56
∴ x = 7

So, number of officer before = 3x
= 3 × 7
= 21