Three people A, B and C working individually can finish a job in 10, 12 and 20 days respectively. They decided to work together but after 2 days, A left the work and after another one day, B also left work. If they got two lacs collectively for the entire work, find the difference of the highest and lowest share.
(A) 70000
(B) 60000
(C) 10000
(D) 20000
Answer: (A)
Explanation: Let the total work be LCM(10, 12, 20) = 60 units
=> Efficiency of A = 60/10 = 6 units / day
=> Efficiency of B = 60/12 = 5 units / day
=> Efficiency of C = 60/20 = 3 units / day
Since the number of working days are different for each person, the share of each will be calculated in the ratio of the units of work done.
Now, A works for 2 days and B works for 3 days.
=> Work done by A = 2 x 6 = 12 units
=> Work done by B = 3 x 5 = 15 units
=> Work done by C = 60 – 12 – 15 = 33 units
Therefore, ratio of work done = 12:15:33 = 4:5:11
So, A’s share = (4/20) x 2,00,000 = Rs 40,000
B’s share = (5/20) x 2,00,000 = Rs 50,000
C’s share = (11/20) x 2,00,000 = Rs 1,10,000
Therefore, difference of the highest and lowest share = Rs 1,10,000 – 40,000 = Rs 70,000
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