Question

A alone can do a piece of work in 12 days and B alone can do the same work in 15 days. They start working together. After 4 days, B leaves the work. In how many days will A alone complete the remaining work?
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Answer 1

Given :

• A alone can do a piece of work in 12 days
• B alone can do the same work in 15 days
• After 4 days , B leaves the work after working together.

To find :

• In how many days A will alone finish the remaining work

Solution :

At first,

In 12 days, A can do work = 1 part

∴ In 1 day, a can do = 1/12 part of work.

Now,

In 15 days, B can do = 1 part of work

∴ In 1 day, B can do = 1/15 part of work.

So, in 1 day :

A and b together can do = (1/12) + (1/15) part of work

                                          = (5 + 4)/60 part of work

                                          = 9/60 part of work

                                          = 3/20 part of work

So they work together for 4 days, so ;

Total work done by both in 4 days = 4 * (3/20) part of work

                                                          = 3/5 part of work

So, work left = (1 - 3/5) part

                     = (5 - 3)/5 part

                     = 2/5 parts

So, A alone has to do = 2/5 parts of work.

Now A alone can do 1 part of work in 12 days.

∴ A alone can do 2/5 parts of work in = (12 * 2/5) days

                                                               = 24/5 days

                                                                = 4.8 days

Therefore,

In 4.8 days , A alone will complete the remaining work.

Answer 2

Answer :-

$\: \: \underline{\boxed{\sf{\green{\mapsto\: \: \: \: Understanding \: the \: Concept}}}}$

Here the concept of Work and Day relationship has been used. We know that number of days taken to complete a work is equal to the fraction of number of day and day taken, which represents the work in one day.

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★ Question :-

A alone can do a piece of work in 12 days and B alone can do the same work in 15 days. They start working together. After 4 days, B leaves the work. In how many days will A alone complete the remaining work?

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★ Solution :-

Given,

» A alone can do a piece of work in 12 days

» B alone can do the same work in 15 days

Then,

$\: \: \longrightarrow \: \: \sf{A \: can \: do \: = \: \bold{\dfrac{1}{12} \: work \: in \: a \: day}}$

$\: \: \longrightarrow \: \: \sf{B \: can \: do \: = \: \bold{\dfrac{1}{15} \: work \: in \: a \: day}}$

So, now according to the question,

A and B start working together so,

➔ Work done by A and B = (1/12) + (1/15)

➔ Work done by A and B = (4 + 5) / 60

➔ Work done by A and B = 9/60

➔ Work done by A and B = 3/20

• So, workdone by A and B, in 4 days :-

$\: \: \: \: \sf{ \: \: \Longrightarrow \: \: \: (A \: and \: B)'s \: work done \: in \: 4 \: days \: = \: 4 \: \times \: \dfrac{3}{20}}$

⟹ Hence, work done by A and B in four days = 3/5

Now remaining work, is given as :-

$\: \: \longrightarrow \: \: \rm{\purple{Remaining \: Work \: = \: 1 \: - \: \dfrac{3}{5}}}$

$\: \: \longrightarrow \: \: \rm{\purple{Remaining \: work \: = \: \dfrac{(5 \: - \: 3)}{5}}}$

$\: \: \longrightarrow \: \: \rm{\purple{Remaining \: Work \: = \: \dfrac{2}{5}}}$

Then, we know that A completes the work in 12 days. So using Unitary Method, we get,

$\: \: \: \: \rm{\orange{\Longrightarrow \: \: No. \: of \: days \: taken \: by \: A \: to \: complete \: the \: work \: = \: \dfrac{2}{5} \: \times \: 12 \: = \: 2 \: \times \: 2.4}}$

➠ No. of days taken by A to complete the work = 2 × 2.4 = 4.8

$\: \: \underline{\boxed{\sf{\blue{No.\:of \: days \: taken \: by \: A \: to \: complete \: the \: work \: alone \: is \: \underline{4.8 \: days}}}}}$

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$\: \: \: \boxed{\rm{\underline{\red{Let's \: know \: more}}}}$

• Time is the standard measure of the change in phases of the day.

• No. of days to day a work, is derived from the relation where work done in one day = reciprocal of number of days required to do the work.