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

Answer 1

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.