Question of the Day :: Boston, Churchill and David :: Time and Work :: Arithmetic Problem

Question is: Boston, Churchill and David are three workers, employed by a contractor. They completed the whole work in 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?

Options:

(a) Rs.900

(b) Rs.1200

(c) Rs.1000

(d) None of the Above.

Answer and Explanation are:
From the above diagram, it is clear that efficiency of C and D is 7.5%, since C and D complete 60% work in 8 days and efficiency of B, C and D is 20%. It mean efficiency of B alone is 20-7.5=12.5%.
Now,
Therefore, Efficiency of C = 5/9 x 7.5 = 4.16%

Efficiency of D = 4/9 x 7.5 = 3.33%

So, D is the least efficient person.
Now share of work done by David(D)=3.333% x 10 = 33.33%
Therefore, his share of amount = 33.33% of Rs.3000 = Rs.1000
Hence, Option(c) is correct.

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