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1. If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work?

A. 60

B. 45

C. 40

D. 30

Solution:

1^st method:
A and B complete a work in = 15 days
One day's work of (A + B) =

\frac{1}{15}

B complete the work in = 20 days;
One day's work of B =

\frac{1}{20}

Then, A's one day's work

\begin{aligned} = \frac{1}{15} - \frac{1}{20} \\ = \frac{4 - 3}{6} \\ = \frac{1}{60} \end{aligned}

Thus, A can complete the work in = 60 days.

2^nd method:
(A + B)'s one day's % work =

\frac{100}{15}

= 6.66%
B's one day's % work =

\frac{100}{20}

= 5%
A's one day's % work = 6.66 - 5 = 1.66%
Thus, A need =

\frac{100}{1.66}

= 60 days to complete the work.

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