Answer
425.1k+ views
Hint: First try to find the fraction of work done by both A and B in one day and then find the fraction of work done by A alone in a day after that find the fraction of work done by B alone in one day. Using the information i.e. fraction of work done by B alone in a day, we can easily find out the amount of time B will take to finish the work alone.
Complete step-by-step answer:
It is given that A and B can do a piece of work in 6 days. Let us suppose the amount of work as X.
If A and B both can finish X amount work in 6 days then, we get that the work done in one day is $ \dfrac{1}{6}th $ of the total amount of work, i.e.
Work done in one day by both A and B = $ \dfrac{X}{6} $
It is also given that A finishes the work in 9 days, hence we get that if A finishes work in 9 days then work done by A in 1 day is $ \dfrac{1}{9}th $ of the total work, so we get
Work done by A alone in 1 day = $ \dfrac{X}{9} $
Now, we know that work done by B alone in one day would be equal to
= (work done by both in 1 day) – (work done by A alone in 1 day)
= $ \dfrac{X}{6} $ - $ \dfrac{X}{9} $
By taking LCM we get,
= $ \dfrac{9X-6X}{9\times 6} $
= $ \dfrac{3X}{54} $
= $ \dfrac{X}{18} $
So, work done by B alone in 1 day is = $ \dfrac{1}{18}th $ of the total amount of work.
Multiplying by 18 on both sides of above expression we get,
Work done by B alone in 18 days = total amount of work
Hence B alone can do the work in 18 days
So, the correct answer is “Option A”.
Note: Be careful while solving this question and don’t try to use any shortcuts here as it can lead to wrong answers.
This question can also be solved by considering amount of work directly for 6 days instead of 1,
For example,
X amount of work is done by both A and B in 6 days,
And $ \dfrac{X}{9} $ amount of work is done by A alone in one day
So, $ \dfrac{6X}{9} $ is the amount of work done by A alone in 6 days
Amount of work done by B in 6 days = work done by both in 6 days – work done by A alone in 6 days
= $ X-\dfrac{6X}{9} $
$ \begin{align}
& =\dfrac{9X-6X}{9} \\
& =\dfrac{3X}{9} \\
& =\dfrac{X}{3} \\
\end{align} $
Hence amount of work done by B alone in 6 days is $ \dfrac{1}{3}rd $ of total work,
So, total work done will be done by B alone in (6 $ \times $ 3) days i.e. 18 days.
Complete step-by-step answer:
It is given that A and B can do a piece of work in 6 days. Let us suppose the amount of work as X.
If A and B both can finish X amount work in 6 days then, we get that the work done in one day is $ \dfrac{1}{6}th $ of the total amount of work, i.e.
Work done in one day by both A and B = $ \dfrac{X}{6} $
It is also given that A finishes the work in 9 days, hence we get that if A finishes work in 9 days then work done by A in 1 day is $ \dfrac{1}{9}th $ of the total work, so we get
Work done by A alone in 1 day = $ \dfrac{X}{9} $
Now, we know that work done by B alone in one day would be equal to
= (work done by both in 1 day) – (work done by A alone in 1 day)
= $ \dfrac{X}{6} $ - $ \dfrac{X}{9} $
By taking LCM we get,
= $ \dfrac{9X-6X}{9\times 6} $
= $ \dfrac{3X}{54} $
= $ \dfrac{X}{18} $
So, work done by B alone in 1 day is = $ \dfrac{1}{18}th $ of the total amount of work.
Multiplying by 18 on both sides of above expression we get,
Work done by B alone in 18 days = total amount of work
Hence B alone can do the work in 18 days
So, the correct answer is “Option A”.
Note: Be careful while solving this question and don’t try to use any shortcuts here as it can lead to wrong answers.
This question can also be solved by considering amount of work directly for 6 days instead of 1,
For example,
X amount of work is done by both A and B in 6 days,
And $ \dfrac{X}{9} $ amount of work is done by A alone in one day
So, $ \dfrac{6X}{9} $ is the amount of work done by A alone in 6 days
Amount of work done by B in 6 days = work done by both in 6 days – work done by A alone in 6 days
= $ X-\dfrac{6X}{9} $
$ \begin{align}
& =\dfrac{9X-6X}{9} \\
& =\dfrac{3X}{9} \\
& =\dfrac{X}{3} \\
\end{align} $
Hence amount of work done by B alone in 6 days is $ \dfrac{1}{3}rd $ of total work,
So, total work done will be done by B alone in (6 $ \times $ 3) days i.e. 18 days.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)