B is 1.5 times as efficient as A. If A can complete $${6 \over 7}$$th of a given task in 12 days, what fraction of the same task would remain incomplete if B works on it independently for 6 days only?
B is 1.5 times as efficient as A. If A can complete $${6 \over 7}$$th of a given task in 12 days, what fraction of the same task would remain incomplete if B works on it independently for 6 days only?
1). $${2 \over 5}$$
2). $${3 \over 5}$$
3). $${4 \over {10}}$$
4). $${5 \over {14}}$$
1 answers
Let efficiency of A = $2x$ units/day
=> Efficiency of B = $1.5 \times 2x = 3x$ units/day
Let Work to be done = 7 units
=> Work done by A in 12 days = $12 \times 2x = \frac{6}{7} \times 7$
=> $24x = 6$
=> $x = \frac{6}{24} = \frac{1}{4}$
Thus, B's 1 day work = $3 \times \frac{1}{4} = \frac{3}{4}$ units
Work done by B in 6 days = $\frac{3}{4} \times 6 = \frac{9}{2}$ units
=> Work left = $7 - \frac{9}{2} = \frac{5}{2}$
$\therefore$ Fraction of work left = $\frac{\frac{5}{2}}{7}$
= $\frac{5}{14}$
