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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
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B
30 hrs
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C
10 hrs
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D
None of the above
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Solution

The correct option is B $$30$$ hrs
Let 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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