Question

A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is:
A. 85
B. 80
C. 75
D. 70

Answer 1

Hint: Question says there are 15 soldiers per captain or for every 15 soldiers there is one captain and we have a total 1200 persons in the train. A group of 15 soldiers plus 1 captain over them makes another group of 16 persons. Dividing 1200 persons by 16, we get the result.

Complete step-by-step answer:
A group of 1200 persons is traveling in a train consisting of captains as well as soldiers. And it is again given that for every 15 soldiers we have one captain. That is it, we make a group of 15 soldiers, then for controlling and instructing them there is one captain. This would make another group consisting both soldiers as well as a captain.
From this question, we can infer that:
\[\text{A group of total 16 persons }\to \text{ 1 person}\]
Therefore,
\[\text{For every 1 person }\to \text{ }\dfrac{1}{16}\text{ captain}\]
If you observe this clearly, it would seem an unrealistic situation that having \[\dfrac{1}{16}\] captain for per person.
But, just for the sake of solving the question and for better understanding we are proceeding this way.
Since, we have \[\dfrac{1}{16}\] captain for 1 person. i.e.
\[\text{For 1 soldier }\to \text{ }\dfrac{1}{16}\text{ captain}\]
Therefore,
\[\begin{align}
  & \text{For 1200 persons }\to \text{ }\dfrac{1}{16}\times 1200 \\
 & \Rightarrow 75 \\
\end{align}\]
So, we have 75 captains in the train.
Therefore, option C is correct.

Note:Students can make very common mistakes by dividing the group of 1200 persons by 15 and get the result 80. This too would be there in the option and this way students can commit mistakes.
\[\begin{align}
  & \dfrac{1200}{15}=80\left( \text{Wrong} \right) \\
 & \dfrac{1200}{16}=75\left( \text{Right} \right) \\
\end{align}\]