Question

Boston, Churchill and David are three workers, employed by a contractor. They completed the whole work in
35.
10 days. Initially all of them worked together, but the last 60% of the work was completed by only Churchill
and David together. Boston worked with Churchill and David only for initial two days then he left the work due
to his poor health. Also Churchill takes 20% less time to finish the work alone than that of David working
alone. If they were paid Rs. 3000 for the entire work then what is the share of least efficient person?

Answer 1

Answer:

take

Step-by-step explanation:

all steps are shown

Answer 2

Rs. 1000

Explanation:

• Let us look at it this way: represent Boston as B, Churchill as C, David as D. therefore;

• $\begin{center}\begin{tabular}{ c c c } initial 2 days & last 8 days & total 10 days \\ B,C,D & C,D & -- \\ 40\% work & 60\% work & -- \end{tabular}\end{center}$

• From the above diagram, it is clear that the efficiency of C and D is 7.5%, since C and D complete 60% of work in 8 days and the efficiency of B, C and D is 20%. It means the efficiency of B alone is $20 - 7.5 = 12.5\%$

• $Therefore\\\\\begin{center}\begin{tabular}{ c c c } \times & C & D \\ n(days) & 4x & 5x \\ \eta & 5y & 4y \end{tabular}\end{center}$

• $\implies \eta(C) = \frac{5}{9} \times 7.5 = 4.16\%\\ \\\\\& \eta(D) = \frac{4}{9} \times 7.5 = 3.33\%$

• $\implies$ David is the least efficient person.

• $share / of / work / of / David(D)=3.333\% \times 10 = 33.33\%\\\\\\Therefore, his share of amount = 33.33\% of Rs.3000 = Rs.1000$