A, B and C can individually complete a piece of work in 30, 50 and 75 days respectively. They worked on one day each, with A starting the work followed by B the next day and C the next day. They continued working like this till the 30th day after which the remaining work was completed by B and C working on alternate days with B working on 31st day. In how many days was the work completed?

1) 50
2) 45
3) 40
4) 35
5) 30

• A+b+c worked on alternative days. So,(1/30)+(1/50)+(1/75)amount of work is completed when 3 had worked one day each, ie equal to 1/15 of the total work. Now they worked for 30 days. So total work they completed is 1/15 * 10 ie equal to 10/15 of the total work.Now remaining work equals 5/15 which is to be completed by B & C. Now b & c together can complete the work in 60 days. So for completing 5/15 of the total work they take (5/15)*60 ie equal to 20 days. So total time taken for completing entire work is 30+20= 50 days.!
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