Question

A can do a work in 12 days and B alone can fo it in 16 days they worked on it for 3 days and A left .how long did B take to finish the remaining work​

Answer 1

Correct Question:

A can do work in 12 days and B alone can do it in 16 days. If they worked on it for 3 days and then A left. How long did B take to finish the remaining work​?

Given:

Two people:-

• A and B

Who can do work for:-

• A = 12 days
• B = 16 days

If they worked for:-

• Both A and B = 3 days

Then A left the work and B did the remaining work.

What To Find:

We have to how long i.e the number of days B takes to finish the remaining work.

How To Find:

To find the number of days, we have to find:-

• Find how much work can A do in 1 day.
• Find how much work can B do in 1 day.
• Add A's and B's work of 1 day.
• Find A's and B's work for 3 days.
• Find the number of days B took to complete the whole work.

Solution:

• For A:-

$\sf \Rightarrow A \: can \: do \: work \: for = 12 \: days$

$\sf \Rightarrow Work \: was \: done \: by \: A \: in \: 1 \: day = \dfrac{1}{12}$

• For B:-

$\sf \Rightarrow B \: can \: do \: work \: for = 16 \: days$

$\sf \Rightarrow Work \: was \: done \: by \: B \: in \: 1 \: day = \dfrac{1}{16}$

• Find the sum for 1 day:-

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 1 \: day = \dfrac{1}{12} +\dfrac{1}{16}$

Take the LCM of 12 and 16 i.e 48,

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 1 \: day = \dfrac{1 \times 4}{12 \times 4} +\dfrac{1 \times 3}{16 \times 3}$

Multiply the numerator and the denominator,

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 1 \: day = \dfrac{4}{48} +\dfrac{3}{48}$

Add the fractions,

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 1 \: day = \dfrac{7}{48}$

• Find the sum of 3 days works:-

Number of works in 1 day by both A and B,

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 1 \: day = \dfrac{7}{48}$

Number of works in 3 days by both A and B,

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 3 \: days = \dfrac{7}{48} \times 3$

Cancel 48 and 3 and it will become 16,

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 3 \: days = \dfrac{7}{16}$

• Find the number of days B took to complete the whole work:-

Find the remaining work,

$\sf \Rightarrow Remaining \: work = 1 - \dfrac{7}{16}$

Take the LCM of 1 and 16 i.e 16,

$\sf \Rightarrow Remaining \: work = \dfrac{1 \times 16 }{1 \times 16} - \dfrac{7 \times 1}{16 \times 1}$

Multiply the numerators and denominators,

$\sf \Rightarrow Remaining \: work = \dfrac{16}{16} - \dfrac{7}{16}$

Subtract the fractions,

$\sf \Rightarrow Remaining \: work = \dfrac{9}{16}$

We know that,

$\sf \Rightarrow B \: can \: do \: work \: for = 16 \: days$

We also know that,

$\sf \Rightarrow B \: can \: do \: \dfrac{9}{16} \: of \: work$

So,

$\sf \Rightarrow Number \: of \: days \: B \: can \: do \: \dfrac{9}{16} \: of \: work = \dfrac{9}{16} \times 16$

Cancel 16 and 16,

$\sf \Rightarrow Number \: of \: days \: B \: can \: do \: \dfrac{9}{16} \: of \: work = 9 \: days$

$\overline {\underbrace {\boxed{ \rm \therefore Therefore, B \: took \: 9 \: days \: to \: finish \: the \: remaining \: work.}}}$

Answer 2

Correct Question:

A can do work in 12 days and B alone can do it in 16 days. If they worked on it for 3 days and then A left. How long did B take to finish the remaining work?

Given:

Two people:-

A and B

Who can do work for:-

A = 12 days

B = 16 days

If they worked for:-

Both A and B = 3 days

Then A left the work and B did the remaining work.

What To Find:

We have to how long i.e the number of days B takes to finish the remaining work.

How To Find:

To find the number of days, we have to find:-

Find how much work can A do in 1 day.

Find how much work can B do in 1 day.

Add A's and B's work of 1 day.

Find A's and B's work for 3 days.

Find the number of days B took to complete the whole work.

Solution:

• For A:-

$\sf \Rightarrow A \: can \: do \: work \: for = 12 \: days$

$\sf \Rightarrow Work \: was \: done \: by \: A \: in \: 1 \: day = \dfrac{1}{12}$

• For B:-

$\sf \Rightarrow B \: can \: do \: work \: for = 16 \: days$

$\sf \Rightarrow Work \: was \: done \: by \: B \: in \: 1 \: day = \dfrac{1}{16}$

• Find the sum for 1 day:-

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 1 \: day = \dfrac{1}{12} +\dfrac{1}{16}$

Take the LCM of 12 and 16 i.e 48,

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 1 \: day = \dfrac{1 \times 4}{12 \times 4} +\dfrac{1 \times 3}{16 \times 3}$

Multiply the numerator and the denominator,

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 1 \: day = \dfrac{4}{48} +\dfrac{3}{48}$

Add the fractions,

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 1 \: day = \dfrac{7}{48}$

• Find the sum of 3 days works:-

Number of works in 1 day by both A and B,

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 1 \: day = \dfrac{7}{48}$

Number of works in 3 days by both A and B,

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 3 \: days = \dfrac{7}{48} \times 3$

Cancel 48 and 3 and it will become 16,

$\sf \Rightarrow Work \: was \: done \: by \: both \: A \: and \: B \: in \: 3 \: days = \dfrac{7}{16}$

• Find the number of days B took to complete the whole work:-

Find the remaining work,

$\sf \Rightarrow Remaining \: work = 1 - \dfrac{7}{16}$

Take the LCM of 1 and 16 i.e 16,

$\sf \Rightarrow Remaining \: work = \dfrac{1 \times 16 }{1 \times 16} - \dfrac{7 \times 1}{16 \times 1}$

Multiply the numerators and denominators,

$\sf \Rightarrow Remaining \: work = \dfrac{16}{16} - \dfrac{7}{16}$

Subtract the fractions,

$\sf \Rightarrow Remaining \: work = \dfrac{9}{16}$

We know that,

$\sf \Rightarrow B \: can \: do \: work \: for = 16 \: days$

We also know that,

$\sf \Rightarrow B \: can \: do \: \dfrac{9}{16} \: of \: work$

So,

$\sf \Rightarrow Number \: of \: days \: B \: can \: do \: \dfrac{9}{16} \: of \: work = \dfrac{9}{16} \times 16$

Cancel 16 and 16,

$\sf \Rightarrow Number \: of \: days \: B \: can \: do \: \dfrac{9}{16} \: of \: work = 9 \: days$

$\overline {\underbrace {\boxed{ \rm \therefore Therefore, B \: took \: 9 \: days \: to \: finish \: the \: remaining \: work.}}}$