Question

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

Answer 1

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

Answer 2

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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