
$A$ can do a piece of work in $24$ days, $A\& B$ can do it in 16 days and $A,B\& C$ in $10\dfrac{2}{3}$ days. In how many days can $A\& C$ do it?
A.$16\dfrac{{24}}{{11}}$
B.$1\dfrac{9}{5}$
C.$13\dfrac{5}{7}$
D.$18\dfrac{3}{8}$
Answer
477k+ views
Hint: These type of problems are solved by following some rule which are-
Suppose if a person can finish a work in $n$ days. Then work done by that person in $1$ day \[ = \] $1/{n^{th}}$part of work.
Suppose that work done by a person in $1$ day is $\dfrac{1}{n}$ then time taken by that person to finish the whole work$ = n$ days.
Complete step-by-step answer:
In the question it is given that
Time taken by $A$ to finish the work $ = 24$ days
Work done by $A$ in 1 day$ = \dfrac{1}{{24}}$
Time taken by $(A + B)$ to finish the work$ = 16$ days
Work done by $(A + B)$in $1$ day$ = \dfrac{1}{{16}}$
Time taken by $\left( {A + B + C} \right)$ to finish the work$ = 10\dfrac{2}{3}$days
$ = \dfrac{{32}}{3}$ days
Work done by $\left( {A + B + C} \right)$ in 1 day$ = \dfrac{3}{{32}}$
Now we can calculate the work done by the $C$ which is
Work done by $\left( {A + B + C} \right)$ in 1 day$ - $Work done by $(A + B)$ in 1 day \[ = \dfrac{3}{{32}} - \dfrac{1}{{16}}\]
$ = \dfrac{{3 - 2}}{{32}} = \dfrac{1}{{32}}$
Now work done by the $C$ in 1 day$ = \dfrac{1}{{32}}$
Further the work done by the $\left( {A + C} \right)$ in 1 day$ = $Work done by $A$ in 1 day$ + $work done by the $C$ in 1 day
$ = \dfrac{1}{{24}} + \dfrac{1}{{32}}$
$ = \dfrac{{4 + 3}}{{96}} = \dfrac{7}{{96}}$
Then the time taken by$\left( {A + C} \right)$to finish work$ = \dfrac{1}{{\left( {\dfrac{7}{{96}}} \right)}}$days
$ = \dfrac{1}{7} \times 96 = \dfrac{{96}}{7}$
$ = 13\dfrac{5}{7}$ days
So, the correct answer is “Option C”.
Note: In these types of questions we can add or subtract quantities of only work done. We cannot add or subtract time which is taken to finish work. We need to avoid any type of calculation mistake.
Suppose if a person can finish a work in $n$ days. Then work done by that person in $1$ day \[ = \] $1/{n^{th}}$part of work.
Suppose that work done by a person in $1$ day is $\dfrac{1}{n}$ then time taken by that person to finish the whole work$ = n$ days.
Complete step-by-step answer:
In the question it is given that
Time taken by $A$ to finish the work $ = 24$ days
Work done by $A$ in 1 day$ = \dfrac{1}{{24}}$
Time taken by $(A + B)$ to finish the work$ = 16$ days
Work done by $(A + B)$in $1$ day$ = \dfrac{1}{{16}}$
Time taken by $\left( {A + B + C} \right)$ to finish the work$ = 10\dfrac{2}{3}$days
$ = \dfrac{{32}}{3}$ days
Work done by $\left( {A + B + C} \right)$ in 1 day$ = \dfrac{3}{{32}}$
Now we can calculate the work done by the $C$ which is
Work done by $\left( {A + B + C} \right)$ in 1 day$ - $Work done by $(A + B)$ in 1 day \[ = \dfrac{3}{{32}} - \dfrac{1}{{16}}\]
$ = \dfrac{{3 - 2}}{{32}} = \dfrac{1}{{32}}$
Now work done by the $C$ in 1 day$ = \dfrac{1}{{32}}$
Further the work done by the $\left( {A + C} \right)$ in 1 day$ = $Work done by $A$ in 1 day$ + $work done by the $C$ in 1 day
$ = \dfrac{1}{{24}} + \dfrac{1}{{32}}$
$ = \dfrac{{4 + 3}}{{96}} = \dfrac{7}{{96}}$
Then the time taken by$\left( {A + C} \right)$to finish work$ = \dfrac{1}{{\left( {\dfrac{7}{{96}}} \right)}}$days
$ = \dfrac{1}{7} \times 96 = \dfrac{{96}}{7}$
$ = 13\dfrac{5}{7}$ days
So, the correct answer is “Option C”.
Note: In these types of questions we can add or subtract quantities of only work done. We cannot add or subtract time which is taken to finish work. We need to avoid any type of calculation mistake.
Recently Updated Pages
How do you solve 05c+3492c4 class 8 maths CBSE

How do you solve dfrac1112dfracn36 class 8 maths CBSE

The value of 015 of 33dfrac13 of Rs10000 is A Rs005 class 8 maths CBSE

Convert 349cm into m class 8 physics CBSE

How do you find the square root of dfrac9144 class 8 maths CBSE

Construct the following quadrilateral Quadrilateral class 8 maths CBSE

Trending doubts
Write a book review which you have recently read in class 8 english CBSE

When Sambhaji Maharaj died a 11 February 1689 b 11 class 8 social science CBSE

Give a character sketch of Griffin the scientist in class 8 english CBSE

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

You want to apply for admission into a prestigious class 8 english CBSE

How many ounces are in 500 mL class 8 maths CBSE
