Question

A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B can do the work in
(A) 12 days
(B) 15 days
(C) 20 days
(D) 30 days

Answer 1

Hint: Assume that A finishes the work in x days. It s given that A is thrice as good a workman as B so, A must be able to finish the work in one-third of the time taken by B. So, \[\text{Time taken by A}\,\text{to finish the work =}\dfrac{\text{Time taken by B}\,\text{to finish the work }}{3}\] . Using this, get the time taken by B to finish the work. Since the time taken by A is 10 less than the time taken by B to finish the work, we have to add 10 days in the time taken by A to make it equal to the time taken by B to finish the work. So,
\[\text{Time taken to finish the work by A+10=Time taken to finish the work by B}\] . Now, using this equation, get the value of x. Now, put the value of x in 3x which is equal to the time taken by B to finish the work.

Complete step-by-step answer:
According to the question, it is given that A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes.
First of all, let us assume that A finishes the work in x days ……………………..(1)
Since A is thrice as good a workman as B so, A must be able to finish the work in one-third of the time taken by B. Mathematically, we can express it as,
\[\text{Time taken by A}\,\text{to finish the work =}\dfrac{\text{Time taken by B}\,\text{to finish the work }}{3}\]……………………..(2)
Now, from equation (1) and equation (2), we get
\[\begin{align}
  & \Rightarrow x\text{=}\dfrac{\text{Time taken by B}\,\text{to finish the work }}{3} \\
 & \Rightarrow 3x=\text{Time taken by B}\,\text{to finish the work} \\
\end{align}\]
The time taken by B to finish the work is \[3x\] days ………………………..(3)
From equation (1) and equation (3), we have the time taken by A and B to finish the work.
It is given that A takes 10 days less than B to finish the work. Since the time taken by A is 10 less than the time taken by B to finish the work, we have to add 10 days in the time taken by A to make it equal to the time taken by B to finish the work. So,
\[\text{Time taken to finish the work by A+10=Time taken to finish the work by B}\] ………………………(4)
Now, from equation (1), equation (3), and equation (4), we get
\[\begin{align}
  & \Rightarrow x\text{+10=}3x \\
 & \Rightarrow 10=3x-x \\
 & \Rightarrow 10=2x \\
\end{align}\]
\[\Rightarrow \dfrac{10}{2}=x\]
\[\Rightarrow 5=x\] ………………………..(5)
Putting the value of x from equation (5), in equation (3), we get
The time taken by B to finish the work = \[3x=3\times 5\] = 15 days.
Therefore, the time taken by B to finish the work is 15 days.
Hence, option (B) is the correct one.

Note: In this question, it is given that A is thrice as good a workman as B. So, one might think that the time taken by A to finish the work is also three times the time taken by B to finish that work. This is wrong because A is thrice as good a workman as B so, A must be able to finish the work in one-third of the time taken by B.