a takes 6 days less than the time taken by b to finish a piece of work if both A and B together can finish it in 4 days.find the time taken by b to finish the work
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Let the number of days taken by A = x
then number of days taken by B = (x + 6)
Work done by A in 1 day = 1/x
Work done by B in one day = 1/(x + 6)
work done by both A and B in 1 day = (1/x) + 1/(x + 6) = (1/4)
[(x+6)+x]/x(x+6) =1/4
4(2x + 6) = x2 + 6x
x2 - 2x - 24 = 0
x2-6x-4x+24=0
x(x-6)-4(x-6)=0
, x = 6 or - 4
as x cannot be negative, therefore x = 6
Thus the time taken by B = x + 6 =6+6= 12 days
then number of days taken by B = (x + 6)
Work done by A in 1 day = 1/x
Work done by B in one day = 1/(x + 6)
work done by both A and B in 1 day = (1/x) + 1/(x + 6) = (1/4)
[(x+6)+x]/x(x+6) =1/4
4(2x + 6) = x2 + 6x
x2 - 2x - 24 = 0
x2-6x-4x+24=0
x(x-6)-4(x-6)=0
, x = 6 or - 4
as x cannot be negative, therefore x = 6
Thus the time taken by B = x + 6 =6+6= 12 days
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