Answer

Verified

440.4k+ views

**Hint:**First we find the one day work for A, B and C.Here a given that the work doing by A and B together and also B and C together so we can split the work of A’s, B’s and C’s Finally, we will find time taken by C to complete the work.

**Complete step-by-step answer:**

Here, it is given that,

A and B together can do a piece of work in 12 days and B and C together do in 16 days

A works for 5 days, B works for 7 days than C completes the remaining work in 13 days

Let’s solve this question arithmetically:

As A and B can finish the work in 12 days’ time, hence

(A + B)’s one day’s work = \[\dfrac{1}{{12}}\]

Similarly

(B + C)’s one day’s work = \[\dfrac{1}{{16}}\]

Now, A’s 5 days’ work + B’s 7 days’ work + C’s 13 days’ work = 1

A’s 5 days’ work + B’s 5 days’ work + B’s 2 days’ work + C’s 2 days’ work + C’s 11 days’ work = 1

Or {(A + B)’s 5 days’ work} + {(B + C)’s 2 days’ work} + C’s 11 days’ work = 1

i.e. $\dfrac{5}{12} + \dfrac{2}{16}$ + C’s 11 days’ work = 1

or C’s 11 days’ work \[ = 1 - \left( {\dfrac{5}{{12}} + \dfrac{2}{{16}}} \right)\]

or C’s 11 days’ work \[ = 1 - \dfrac{{13}}{{24}}\]

or C’s 11 days’ work \[ = \dfrac{{11}}{{24}}\]

or C’s 1 day’s work \[ = \dfrac{{11}}{{24}} \times \dfrac{1}{{11}} = \dfrac{1}{{24}}\]

Therefore, C alone can finish the complete work in 24 days.

**Note:**Mathematically we say that if A can complete a work in n days, work done by A in \[1\] day is \[\dfrac{1}{n}\]. And if A can complete \[\dfrac{1}{n}\] part of the work in \[1\] day, then A will complete the work in n days.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Onam is the main festival of which state A Karnataka class 7 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Who was the founder of muslim league A Mohmmad ali class 10 social science CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers