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1. A and B together can complete a work in 3 days. They start together but after 2 days, B left the work. If the work is completed after two more days, B alone could do the work in

A. 5 days

B. 6 days

C. 9 days

D. 10 days

Solution:

1^st Method:
(A+B)'s one day's work =

\frac{1}{3}

part
(A+B) works 2 days together =

\frac{2}{3}

part
Remaining work =

1 - \frac{2}{3}

\frac{1}{3}

part

\frac{1}{3}

part of work is completed by A in two days
Hence, one day's work of A =

\frac{1}{6}

Then, one day's work of B =

\frac{1}{3} - \frac{1}{6}

\frac{1}{6}

So, B alone can complete the whole work in 6 days.

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

\frac{100}{3}

= 33.3%
Work completed in 2 days = 66.6%
Remaining work = 33.4%
One day's % work of A =

\frac{33.4}{2}

= 16.7%
One day's work of B = 33.4 - 16.7 = 16.7%
B alone can complete the work in,
=

\frac{100}{16.7}

= 5.98 days
≈ 6 days.

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