Question

# For the same amount of work , A takes 6 hours less than B. If together they complete the work in 13 hours 20 minutes; find how much time will B alone take to complete the work.

A
20 hrs
B
30 hrs
C
10 hrs
D
None of the above

Solution

## The correct option is B $$30$$ hrsLet the time taken to complete the work  by B be  x.A can take x - 6 hours.A and B together can complete the work = 13 hours 20 minutes.$$\frac{1}{x-6}+\frac{1}{x}=13\frac{20}{60}$$$$\frac{2x-6}{x^2-6x}=\frac{3}{40}$$$$40(2x-6)=3x^2-18x$$$$80x-240=3x^2-18x$$$$3x^2-98x+240$$Using quadratic formula, $$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$$$\frac{98\pm\sqrt{(-98)^2-4\times 3\times 240}}{2\times 3}$$$$\frac{98\pm\sqrt{6724}}{6}$$$$\frac{98\pm 82}{6}$$So, x = 30, x = 2.6666..x value cannot be negative.B take 30 hours to complete the work alone.Mathematics

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