Remaining senseless

Algebra Level pending

Suppose , the scientists of NASA have found a special planet outside the solar system . There are two gases in that planet named 'Alpha' and 'Beta' . When both of those gases or just one of them remain(s) at an optimum level , the planet is quite livable for any animal of Earth . But when none of the gases remain at their optimum level , a corrosive environment gets created in the planet that makes any animal senseless in the planet for a whole day . After leaving a dog in the planet for 60 days , the scientists get to know that in those 60 days , 'Alpha' gas remained at it's optimum level in total 18 days and 'Beta' gas remained at it's optimum level in total 26 days . But as the scientists didn't know in how many days , the dog was senseless in the planet , they found an average possible number of it in respect of the highest possible number and the lowest possible number of days of the dog's remaining senseless in that planet . Find the average possible number .


The answer is 25.

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1 solution

Saya Suka
Jan 19, 2021

Minimum senseless day
= 60 - (no overlapping days of optimal gasses)
= 60 - (18 + 26)
= 60 - 44
= 16


Maximum senseless day
= 60 - (maximal overlapping days of optimal gasses)
= 60 - { max(18, 26) }
= 60 - 26
= 34

Average senseless days
= (16 + 34) / 2
= 25

I solved it with the help of Venn-diagram . However , the calculation was same at the end......

Sudipto Podder - 4 months, 3 weeks ago

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