Question

A garrison of 900 soldiers had food-stock sufficient
for 30 days when the rate of consumption is
2.5 kg/day/soldier. After some days of consumption
at that rate, 300 soldiers were transferred to another
garrison and the balance food lasted for 25 days for
the remaining soldiers. If the rate of consumption of
the remaining soldiers was 3.0 kg/day/ soldier, after
how many days from the start, were the soldiers
transferred?

Answer 1

Answer:

Step-by-step explanation:

The quantity of the balance of food after the transfer is such that

(900 -300) =600 soldiers, consumed at the rate of 3 kg/day/soldier, for 25 days.

If the soldiers were not transferred, 900 soldiers would have consumed it at the rate of 2.5 kg/day/soldier, the same food.  

The data can be tabulated as:

Soldiers         Consumption rate              Number of days

600                        3.0                                  25

900                        2.5                               How many?

Number of soldiers and the number of days for which food lasts are inversely proportional. The number of soldiers increased;

hence, number of days decreases.  

Hence multiplication factor is (600/900).

Consumption rate and number of days are also inversely proportional.  

Hence, multiplication factor is 3.0/2.5

Applying the above rates of variation,  

the number of days =25×(600/900)×(3.0/2.5) =20 days

The initial stock was to last for 30 days.

⇒Soldiers were transferred after 30 -20 =10 days