B is $${4 \over 3}$$ times as efficient as A. If A can complete $${5 \

1.	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). $${4 \over 9}$$
Answer» Solution 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 = $\frac{\frac{32}{9}}{8}$ = $\frac{4}{9}$

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). $${4 \over 9}$$

Answer»

Solution

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 = $\frac{\frac{32}{9}}{8}$

= $\frac{4}{9}$