plz help problem sum..
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Let the no . Of days taken be x days.
A/q,when all 150 workers work it takes 8less days .
Total work =150(x-8)..(i)
Now,if 4 workers dropped on 2nd day,4 more workers on 3rd day and so on..then no. Of workers decreases by 4 each day i.e common difference=-4
Total work =x/2[2(150)+(x-1)(-4)]
=x/2(300-4x+4)
=x/2(304-4x)=x(152-2x). ...(ii)
From eq. (i) and (ii),
=>150(x-8)=x(152-2x)
=>150x-1200=152x-2x^2
=>2x^2-2x-1200=0.
=>x^2-x-600=0
=>x^2-25x+24x-600=0
=>x(x-25)+24(x-25)=0
=>x=25 or x=-24
But the no of days can't be negative
So,x=25.
So,no. Of days taken =25 days
A/q,when all 150 workers work it takes 8less days .
Total work =150(x-8)..(i)
Now,if 4 workers dropped on 2nd day,4 more workers on 3rd day and so on..then no. Of workers decreases by 4 each day i.e common difference=-4
Total work =x/2[2(150)+(x-1)(-4)]
=x/2(300-4x+4)
=x/2(304-4x)=x(152-2x). ...(ii)
From eq. (i) and (ii),
=>150(x-8)=x(152-2x)
=>150x-1200=152x-2x^2
=>2x^2-2x-1200=0.
=>x^2-x-600=0
=>x^2-25x+24x-600=0
=>x(x-25)+24(x-25)=0
=>x=25 or x=-24
But the no of days can't be negative
So,x=25.
So,no. Of days taken =25 days
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