Answer
Verified
394.5k+ views
Hint: Let us assume that $A$ alone can do the work in $x$ days and similarly $B$ alone can do the same work in $y$ days.
Then one day work of $A$$ = \dfrac{1}{x}$
One day work of $B$$ = \dfrac{1}{y}$
Now we have to do the rest calculation.
Complete step-by-step answer:
In this question it is given that $A$ and $B$ can do a piece of work in $15$ days. It is also given that $A$’s one day work is $1\dfrac{1}{2}$ times the one day work of $B$.
Now we have to calculate the total time taken by $A$ alone and $B$ alone to do this work.
So first of all let us assume that:
$A$ alone can do the work in $x$ days.
$B$ alone can do the same work in $y$ days.
So if $A$ alone can do the work in $x$ days, then one day work of $A$$ = \dfrac{1}{x}$
And if $B$ alone can do the same work in $y$ days, then one day work of $B$$ = \dfrac{1}{y}$
And in this question we know the relation between both one day’s work.
$A$’s one day work is $1\dfrac{1}{2}$ times the one day work of $B$.
Here we know that
One day work of $A$$ = \dfrac{1}{x}$
One day work of $B$$ = \dfrac{1}{y}$
And $\dfrac{1}{x} = 1\dfrac{1}{2}.\dfrac{1}{y}$
$\dfrac{1}{x} = \dfrac{3}{{2y}}$
$y = \dfrac{{3x}}{2}$ $ - - - - - \left( 1 \right)$
Now it is also given that they can complete work together in $15$ days. So one day work of together is:
$\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{{15}}$ $ - - - - - \left( 2 \right)$
Now putting the value of $y = \dfrac{{3x}}{2}$ in equation $\left( 2 \right)$
$\dfrac{1}{x} + \dfrac{2}{{3x}} = \dfrac{1}{{15}}$
$\dfrac{{3 + 2}}{{3x}} = \dfrac{1}{{15}}$
$\dfrac{5}{{3x}} = \dfrac{1}{{15}}$
$x = 25$days
Similarly $y = \dfrac{{3x}}{2}$$ = \dfrac{{75}}{2}$ days
So $A$ alone can do the work in $25$ days.
$B$ alone can do it in $\dfrac{{75}}{2}$ days.
Note: In this type of question you need to find the two questions. First equation you will get from the statement that they can complete work together in $15$ days. And the second equation, you will get from the statement that $A$’s one day work is $1\dfrac{1}{2}$ times the one day work of $B$.
Then one day work of $A$$ = \dfrac{1}{x}$
One day work of $B$$ = \dfrac{1}{y}$
Now we have to do the rest calculation.
Complete step-by-step answer:
In this question it is given that $A$ and $B$ can do a piece of work in $15$ days. It is also given that $A$’s one day work is $1\dfrac{1}{2}$ times the one day work of $B$.
Now we have to calculate the total time taken by $A$ alone and $B$ alone to do this work.
So first of all let us assume that:
$A$ alone can do the work in $x$ days.
$B$ alone can do the same work in $y$ days.
So if $A$ alone can do the work in $x$ days, then one day work of $A$$ = \dfrac{1}{x}$
And if $B$ alone can do the same work in $y$ days, then one day work of $B$$ = \dfrac{1}{y}$
And in this question we know the relation between both one day’s work.
$A$’s one day work is $1\dfrac{1}{2}$ times the one day work of $B$.
Here we know that
One day work of $A$$ = \dfrac{1}{x}$
One day work of $B$$ = \dfrac{1}{y}$
And $\dfrac{1}{x} = 1\dfrac{1}{2}.\dfrac{1}{y}$
$\dfrac{1}{x} = \dfrac{3}{{2y}}$
$y = \dfrac{{3x}}{2}$ $ - - - - - \left( 1 \right)$
Now it is also given that they can complete work together in $15$ days. So one day work of together is:
$\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{{15}}$ $ - - - - - \left( 2 \right)$
Now putting the value of $y = \dfrac{{3x}}{2}$ in equation $\left( 2 \right)$
$\dfrac{1}{x} + \dfrac{2}{{3x}} = \dfrac{1}{{15}}$
$\dfrac{{3 + 2}}{{3x}} = \dfrac{1}{{15}}$
$\dfrac{5}{{3x}} = \dfrac{1}{{15}}$
$x = 25$days
Similarly $y = \dfrac{{3x}}{2}$$ = \dfrac{{75}}{2}$ days
So $A$ alone can do the work in $25$ days.
$B$ alone can do it in $\dfrac{{75}}{2}$ days.
Note: In this type of question you need to find the two questions. First equation you will get from the statement that they can complete work together in $15$ days. And the second equation, you will get from the statement that $A$’s one day work is $1\dfrac{1}{2}$ times the one day work of $B$.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Assertion CNG is a better fuel than petrol Reason It class 11 chemistry CBSE
How does pressure exerted by solid and a fluid differ class 8 physics CBSE
Number of valence electrons in Chlorine ion are a 16 class 11 chemistry CBSE
What are agricultural practices? Define
What does CNG stand for and why is it considered to class 10 chemistry CBSE
The rate of evaporation depends on a Surface area b class 9 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
State whether the following statement is true or false class 11 physics CBSE
A night bird owl can see very well in the night but class 12 physics CBSE