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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