Question

Q. A can do a piece of in 20 days b it in 15 days. They work together on it for 6 days and then a left. How long will take tofinish the remaining work ?
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Answer 1

Given:

• A can do a piece of in 20 days
• B can do it in 15 days
• They work together for 6 days and then A left

To Find:

• How long will B take to finish the remaining work ?

Solution:

⊱let's start:

$: \longrightarrow \tt \: let \: a's \: 1 \: days \: work = \frac{1}{20} \\ \\ : \longrightarrow \tt \: let \: b's \: 1 \: days \: work = \frac{1}{15}$

Now, the work done by a and b in one day :

$\longmapsto \frac{1}{20} + \frac{1}{15} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longmapsto \frac{1 \times 3}{20 \times 3} + \frac{15 \times 4}{20 \times 4} \\ \\ \\ \longmapsto \frac{3}{60} + \frac{4}{60} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longmapsto \frac{3 + 4}{60} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longmapsto \frac{7}{60} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

★Now the work done by and and b for 6 days★

$\longmapsto \: 6 \times \frac{7}{60} \: \: \: \: \: \\ \\ \\ \longmapsto \cancel{ 6 }^{1} \times \frac{7} {\cancel{60}^{10} } \\ \\ \\ \longmapsto \frac{7}{10} \bigstar \: \: \: \: \: \: \: \: \:$

⇨ Now the remaining work

${: \implies}\sf \frac{1}{1} - \frac{7}{10} \: \: \\ \\ \\ \\ {: \implies}\sf \frac{10}{10} - \frac{7}{10} \\ \\ \\ \\ {: \implies}\sf \frac{3}{10} \star \: \: \: \: \: \: \:$

as b can do a work in 15days the work done by b in 3/10 days:

$\leadsto15 \times \frac{3}{10} \\ \\ \leadsto \cancel\frac{45}{10} \: \: \: \: \: \: \: \: \: \\ \\ \leadsto \sf 4.5days$

$\blue{ \underline{ \boxed{ \pink{ \mathfrak{ \therefore \: b \: takes \: 4.5 \: days \: to \: do \: the \: work} \: \bigstar}}}}$

Answer 2

➲Given that, A can do a piece of work in 20 days b can do the same work in 15 days.

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To Find:

⊱They work together on it for 6 days and then a left.

• How long will take b to finish the remaining work ?

Solution:

Now,

$\rm \: \leadsto \: the \: work \: done \: by \: A\: per \: day = \frac{1}{20} \\ \\ \\ \rm \leadsto \: the \: work \: done \: by \: B\: per \: day = \frac{1}{15}$

as given a and b worked together

${ : \longrightarrow} \tt \: their \: work \: done \: togeather \: per \: day \: = \frac{1}{20} + \frac{1}{15} \\ \\ \\ \\ { : \longrightarrow} \tt \: their \: work \: done \: togeather \: per \: day \: = \frac{3 + 4}{60} \: \: \: \: \\ \\ \\ \\ { : \longrightarrow} \tt \: their \: work \: done \: togeather \: per \: day \: = \frac{7}{60} \: \: \: \: \: \: \: \: \:$

A and B worked together for 6 days so the work done:

$\longmapsto \: \frac{7}{60} \times 6 \: \: \\ \\ \\ \longmapsto \frac{7}{10} \: \: \: \: \: \: \: \: \:$

so, the work left equals.

$\leadsto \frac{1}{1} - \frac{7}{10} \\ \\ \\ \leadsto \frac{3}{10} \: \: \: \: \: \: \:$

B has the capacity to do the whole work in 15 days so 3/10th of the work can be done in

$\frac{3}{10} \times 15 \: \\ \\ \tt4.5days$

${\therefore }\rm{\underline{ \: b \: can \: do \: the \: leftover \: work \: in \: 4.5 \: days}}$

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