The amount of job that Amal, Sunil and Kamal can individually do in a day, are inĀ harmonic progression. Kamal takes twice as much time as Amal to do the sameĀ amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, KamalĀ needs to work for 16 days to finish the remaining job. Then the number of daysĀ Sunil will take to finish the job working alone, is
Correct Answer: 27
Let us assume the efficiencies of Amal, Sunil, and Kamal are a, s, and k, respectively.
Given that they are in H.P.
=> $$\dfrac{2}{s}=\dfrac{1}{a}+\dfrac{1}{k}$$ ---(1)
Also, given that Kamal takes twice as much time as Amal to do the same amount of job
=> a = 2k
Given that when Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job.
=> If W is the total work => 4a + 9s + 16k = W.
from (1)$$\dfrac{2}{s}=\dfrac{1}{a}+\dfrac{2}{a}$$ => $$a=\dfrac{3}{2}s$$ and $$k=\dfrac{3}{4}s$$
=> $$4\left(\dfrac{3s}{2}\right)+9s+16\left(\dfrac{3s}{4}\right)=W$$
=> $$6s+9s+12s=W$$
=> $$27s=W\ =>\ s\ =\ \dfrac{W}{27}$$
=> Sunil will take 27 days to finish the work when working alone.
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