Answer
Verified
424.5k+ views
Hint: Take the number of days taken by B as $x$ and that of A as $\dfrac{x}{2}$ as it is mentioned in the question that A is twice as efficient as B. Then find the work completed by both in one day and equate their sum by $\dfrac{1}{42}$. Then find the number of days taken by B and after that find the number of days taken by A, which is the answer.
Complete step-by-step answer:
In the question, it is given that A is twice as good a workman as B, which means that A is twice as efficient as B. So, if we say that B takes $x$ amount of time to do a work, then A takes $\dfrac{x}{2}$ amount of time to do the same work.
Now, let us suppose that B takes $x$ days to complete a work, then we can say that in 1 day B completes $\dfrac{1}{x}$ amount of work.
Now, as we know that B takes $x$ days, then A will take $\dfrac{x}{2}$ days to complete the work. So, we can say that in 1 day A completes $\dfrac{2}{x}$ amount of work.
If A and B work together, then it takes them 14 days to complete the work. So, we can say that in 1 day A and B complete $\dfrac{1}{14}$ amount of work.
In terms of $x$, A and B complete $\left( \dfrac{1}{x}+\dfrac{2}{x} \right)$ or $\dfrac{3}{x}$ amount of work in 1 day. So, we can equate $\dfrac{3}{x}$ and $\dfrac{1}{14}$ as they represent the same quantities. So, we get,
$\begin{align}
& \dfrac{3}{x}=\dfrac{1}{14} \\
& \Rightarrow 3\times 14=x \\
& \Rightarrow x=42 \\
\end{align}$
Hence, B takes 42 days to complete the work. As it is mentioned in the question that A is twice as efficient as B, so A takes $\dfrac{42}{2}=21$ days to complete the work.
Therefore, the correct option is D.
Note: Instead of taking $x$ as the number of days taken by B, we can take it as the number of days taken by A. In that case, B will take $2x$ days as A is twice as efficient as B. So, the equation will be, $\dfrac{1}{x}+\dfrac{1}{2x}=\dfrac{1}{14}$ and by simplifying, we get the direct value of the number of days taken by A, which is 21 days.
Complete step-by-step answer:
In the question, it is given that A is twice as good a workman as B, which means that A is twice as efficient as B. So, if we say that B takes $x$ amount of time to do a work, then A takes $\dfrac{x}{2}$ amount of time to do the same work.
Now, let us suppose that B takes $x$ days to complete a work, then we can say that in 1 day B completes $\dfrac{1}{x}$ amount of work.
Now, as we know that B takes $x$ days, then A will take $\dfrac{x}{2}$ days to complete the work. So, we can say that in 1 day A completes $\dfrac{2}{x}$ amount of work.
If A and B work together, then it takes them 14 days to complete the work. So, we can say that in 1 day A and B complete $\dfrac{1}{14}$ amount of work.
In terms of $x$, A and B complete $\left( \dfrac{1}{x}+\dfrac{2}{x} \right)$ or $\dfrac{3}{x}$ amount of work in 1 day. So, we can equate $\dfrac{3}{x}$ and $\dfrac{1}{14}$ as they represent the same quantities. So, we get,
$\begin{align}
& \dfrac{3}{x}=\dfrac{1}{14} \\
& \Rightarrow 3\times 14=x \\
& \Rightarrow x=42 \\
\end{align}$
Hence, B takes 42 days to complete the work. As it is mentioned in the question that A is twice as efficient as B, so A takes $\dfrac{42}{2}=21$ days to complete the work.
Therefore, the correct option is D.
Note: Instead of taking $x$ as the number of days taken by B, we can take it as the number of days taken by A. In that case, B will take $2x$ days as A is twice as efficient as B. So, the equation will be, $\dfrac{1}{x}+\dfrac{1}{2x}=\dfrac{1}{14}$ and by simplifying, we get the direct value of the number of days taken by A, which is 21 days.
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
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with proper collective nouns 1 A of class 10 english CBSE
What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Net gain of ATP in glycolysis a 6 b 2 c 4 d 8 class 11 biology CBSE
What organs are located on the left side of your body class 11 biology CBSE