Question

An army base camp had provisions for 150 soldiers for 45 days. After 10 days 25 soldiers left the camp. How long will the food last at the same rate? Rajan cycles to his school at an average speed of 12 km/hr. He takes 20 minutes so find the distance he covered in meters.

Answer 1

Hint – In this particular question use the concept that assume any variable be the number of day’s food last for the remaining soldiers and later on in the solution use that multiplication of this variable with the remaining soldiers is equal to the original number of soldiers and the remaining days so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given data:
Total number of soldiers = 150
Food lasts for = 45 days.
Now after 10 days 25 soldiers left.
So the remaining days = (45 – 10) = 35 days.
Remaining soldiers = (150 – 25) = 125 soldiers.
Now we have to find out how long the food lasts at the same rate.
Let the food last for X number of days.
So the multiplication of X with the remaining soldiers is equal to the original number of soldiers and the remaining days.
Therefore, $X\times 125=150\times 35$
Now simplify this we have,
$\Rightarrow X={\displaystyle \frac{150\left(35\right)}{125}}={\displaystyle \frac{6\left(35\right)}{5}}=6\left(7\right)=42$ Days.
So the food lasts for 42 days.
Now the average speed of the Rajan = 12km/hr.
As we know 1 km = 1000 m and 1hr = 60 min.
So 1 km/hr. = (1000/60) = (50/3) m/min.
So 12 km/hr. = $12\times {\displaystyle \frac{50}{3}}=200$ m/min.
Now it is given it takes 20 min to cover.
Now as we know that the distance (S) covered by him is the product of his average speed and the time taken.
Therefore, S = 200(20) = 4000 m = 4 km.
So this is the required answer.

Note – Whenever we face such types of questions the key concept we have to remember is that the relation between speed, distance and time, as distance is the product of the speed and the time taken, so using this formula calculate the distance covered by the Rajan as above we will get the required answer.