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. 8
• B. 40 hrs
• C. 10 hrs
• D. 15 hrs

Answer 1

The correct option is A

8

If B alone takes x hours then A alone takes (x - 6) hours for the same work.

$\therefore$ $\frac{1}{x-6}+\frac{1}{x}=\frac{3}{40}$ [ 13 hours 20 min = $\frac{40}{3}$ ]

$\to$ $\frac{x+x-6}{(x-6)x}=\frac{3}{40}$

$\to$ $3x^2-18x=80x-240$

$3x^2-98x+240=0$

$3x^2-90x-8x+240=0$

$(x-30)(3x-8)=0$

$\to$ x = 30 or x = $\frac{8}{3}$

Since, time can't be in fraction

$\therefore$ B alone will take 30 hrs to complete the work.