an army of250 soliders had provision for 44 days . afresh batch 300 soliders joined the camp .for how many days will the provision last ( direct and indirect proportional
Answers
You didn't mentioned after how many days fresh batch joined. So I am assuming first day itself they joined.
let us take n as the amount of provision for one soldiers for one day
provision for 250 soldiers for 44days = 250*44*n = 11000n
No of total soldiers = 250 + 300 = 550
Food needs for 550 soldiers for one day = 550n
No of days will the provision last = 11000/550 = 20days
The provision of food will last for 20 days.
Given:
number of soldiers = 250
extra soldiers added = 300
number of days of food available for 250 soldiers = 44 days
To Find:
the number of days for which the food will last now that 300 soldiers are added
Solution:
let the total food available be x
250 soldiers can consume the food available in 44 days
then, food consumed by 1 soldier in 1 day will be = x/(44 × 250)
now, new number of soldiers = 300 + 250 = 550
⇒ food consumed by 550 soldiers in 1 day = x/(44 × 250) × 550
= 550x/11000
= 0.05x
now, the let n be the number of days for which the food lasts
⇒ 0.05x × n = x
0.05n = 1
n = 1/0.05
n = 20
Thus, the provision of food will last for 20 days.
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