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A, B and C can together complete a work in 20 days. On the other hand, B and C can together complete the work in 30 days, while C can complete the work alone in 50 days. If A left when the work was 20% complete, while B left when the work was 50% complete, and C completed rest of the work alone, in how many days will the work be complete?

A, B and C can together complete a work in 20 days. On the other hand, B and C can together complete the work in 30 days, while C can complete the work alone in 50 days. If A left when the work was 20% complete, while B left when the work was 50% complete, and C completed rest of the work alone, in how many days will the work be complete? Correct Answer 38 days

A left when the work was 20% complete, this means that A, B and C worked together to complete 20% of the work,

∵ A, B and C can together complete the work in 20 days,

⇒ Time taken by A, B and C to complete 20% of the work = 20% of 20 = 1/5 × 20 = 4 days

Now, B left when the work was 50% complete, this means that B and C worked together to complete 50 – 20 = 30% of the work,

∵ B and C can together complete the work in 30 days,

⇒ Time taken by B and C to complete 30% of the work = 30% of 30 = 3/10 × 30 = 9 days

And finally, C completed the remaining work, this means that C worked alone to complete 100 – 50 = 50% of the work,

∵ C can complete the work alone in 50 days,

⇒ Time taken by C to complete 50% of the work = 50% of 50 = 1/2 × 50 = 25 days

∴ The work will be complete in = 4 + 9 + 25 = 38 days

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