B is $${4 \over 3}$$ times as efficient as A. If A can complete $${5 \over 8}$$th of a given task in 15 days, what fraction of the same task would remain incomplete if B works on it independently for 10 days only?
1). $${3 \over 4}$$
2). $${2 \over 3}$$
3). $${5 \over 8}$$
4). $${4 \over 9}$$
Let efficiency of A = $3x$ units/day
=> Efficiency of B = $\frac{4}{3} \times 3x = 4x$ units/day
Let Work to be done = 8 units
=> Work done by A in 15 days = $15 \times 3x = \frac{5}{8} \times 8$
=> $45x = 5$
=> $x = \frac{5}{45} = \frac{1}{9}$
Thus, B's 1 day work = $4 \times \frac{1}{9} = \frac{4}{9}$ units
Work done by B in 10 days = $\frac{4}{9} \times 10 = \frac{40}{9}$ units
=> Work left = $8 - \frac{40}{9} = \frac{32}{9}$
$\therefore$ Fraction of work left = $\frac{\frac{32}{9}}{8}$
= $\frac{4}{9}$