Question

A, B and C are employed to do a piece of work for Rs. 529. A and B together are supposed to do $ \dfrac{19}{23} $ of the work, and B and C together $ \dfrac{8}{23} $ of the work. What amount should A be paid?
a. Rs. 315
b. Rs. 345
c. Rs. 355
d. Rs. 375

Answer 1

Hint: We will use the concept that the sum of all fractions is equal to 1, that is, the fraction of sum of work done by A, B and C will be equal to 1. So, we will get, $ A+B+C=\dfrac{23}{23}=1 $ . We will first calculate the work done by A as, $ A+B+C=1\Rightarrow A+\left( \dfrac{8}{23} \right)=1\Rightarrow A=1-\dfrac{8}{23} $ . From this, we will get the ratio of A and (B+C) as 15:8. Finally, we will calculate the amount of A as $ \dfrac{\text{work done by A}}{\text{total work done by A,B,C}}\text{ }\!\!\times\!\!\text{ total amount} $ .

Complete step-by-step answer:
It is given in the question that A, B and C are employed to do a piece of work for Rs. 529. A and B together are supposed to do $ \dfrac{19}{23} $ of the work, and B and C together $ \dfrac{8}{23} $ of the work. And we have been asked to find the amount A should get.
We know that the total amount is equal to Rs. 529. So, we can write, $ A+B+C=Rs.529 $ .
Now, we have been given that A and B do $ \dfrac{19}{23} $ of the work, so we can write,
 $ A+B=\dfrac{19}{23}.........(i) $
Also, we have been given that, B and C do $ \dfrac{8}{23} $ of the work. So, we can write,
 $ B+C=\dfrac{8}{23}.........(ii) $
Now, we know that the sum of all the fractions must be equal to 1. So, we can write,
 $ A+B+C=1.........(iii) $
From equation (ii), we get the value of $ B+C=\dfrac{8}{23} $ . So, on substituting the value of (B+C) in equation (iii), we will get,
 $ A+\dfrac{8}{23}=1 $
On transposing $ \dfrac{8}{23} $ from the LHS to RHS, we get,
 $ A=1-\dfrac{8}{23} $
On taking the LCM of the terms in the RHS, we get,
 $ \begin{align}
  & A=\dfrac{23-8}{23} \\
 & A=\dfrac{15}{23} \\
\end{align} $
So, we can write the ratio, A: (B+C) as,
 $ \begin{align}
  & A:\left( B+C \right)=\dfrac{15}{23}:\dfrac{8}{23} \\
 & A:\left( B+C \right)=15:8 \\
\end{align} $
Now, we have been asked to find the amount that A will get for the work A does. So, it can be calculated as follows,
 $ \begin{align}
  & \dfrac{\text{work done by A}}{\text{total work done by A,B,C}}\text{ }\!\!\times\!\!\text{ total amount} \\
 & \text{=}\dfrac{15}{15+8}\times 529 \\
 & =\dfrac{15}{23}\times 529 \\
 & =15\times 23 \\
 & =Rs.345 \\
\end{align} $
Therefore, the amount that A will get for the work A does will be Rs. 345.

Note: The most common mistake that the students make while solving this question is that, they take the sum of A, B and C as, $ \dfrac{19}{23}+\dfrac{8}{23}=\dfrac{27}{23} $ , which is wrong as, here B’s work done is repeating in both the fractions. So, these kinds of mistakes must be avoided. Also, the sum of the fractions must be taken as equal to 1 and not equal to 529, as 529 is the total amount of A, B and C.