# 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 regiment before battle was = ?

• 131
• 238
• 321
• 428
Explanation:-

Solution:
Let the number of officers and soldiers = 3x, 31x
According to the question,
$\begin{array}{rl}& ⇒\frac{3x-6}{31x-22}=\frac{1}{13}\\ & ⇒39x-78=31x-22\\ & ⇒8x=56\\ & ⇒x=7\end{array}$
So, number of officer before
= 3x = 3 × 7 = 21

$\begin{array}{rl}& ⇒\frac{3x-6}{31x-22}=\frac{1}{13}\\ & ⇒39x-78=31x-22\\ & ⇒8x=56\\ & ⇒x=7\end{array}$