Question

A can do a piece of work in 20 days and b in 25 days. They work together for 5 days then b goes away. In how many days will a complete the ramaining work

Answer 1

$\bf {\huge {\underline {\boxed {\sf\purple {Answer:\: {13}\dfrac {3}{5}\: days }}}}}$

$\textbf {\underline{\underline{Step-By-Step\:Explanation:-}}}$

● $\textbf{\pink {\underline{Given:}}}$

• A can do a piece of work in 20 days
• B can do in 25 days
• They both worked together for 5 days
• Then, B goes away.

● $\textbf {\underline {\underline {To\:Find:}}}$

• A can finish the work in how many of days

$\huge\underline\green {\tt Solution:}$

Let work done be ' w '

Now,

➡ Work done by A in 20 days

= $\dfrac{w}{20}$ ------ ( of 1 day )

➡ Work done by B in 25 days

= $\dfrac {w}{25}$ ----- ( of 1 day )

When they worked together,

$= \frac{5w}{20} + \frac{5w}{25}$

= $\cancel{\dfrac{5}{20}} + \cancel{\dfrac {5}{25}}$

$= \frac{w}{4} + \frac{w}{5}$

$= \frac{9w}{20}$

Now,

After B left the work,

$= w - \frac{9w}{20}$

$= > \frac{20w - 9w}{20} = \: \frac{11w}{20}$

•°• $\dfrac{11w}{20}$ is to be done by B. Therefore,

$= \frac{11w}{20} \times \frac{25}{w} \\ \\ = \frac{55}{4} \\ \\ = 13 \times \frac{3}{5}$

= 13. 75 days

Answer : A will take ${13}\dfrac {3}{5}$ days.

Answer 2

Answer:

• A will complete his work in 11 days.

Step-by-step explanation:

Work done by A in one day

$= \frac{1}{20}$

Work done by B in one day

$= \frac{1}{25}$

Work done by A and B in one day

$= \frac{1}{20} + \frac{1}{25} \\ = \frac{9}{100}$

Work done by A and B five days

$= 5 \times \frac{9}{100} = \frac{9}{20}$

Remaining work

$= 1 - \frac{9}{20} = \frac{11}{20}$

$\frac{1}{20} \: work \: is \: done \: by \: a \: in \: one \: day. \\ \frac{11}{20 } \: \: work \: is \: done \: by \: a \: in \: one \: day \:$

$= \frac{11}{20} \times \frac{20}{1} \\ = 11days$