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A and B can finish a job in 10 days while B and C can do it in 18 days. A started the job, worked for 5 days then B worked for 10 days and the remaining job was finished by C in 15 days. In how many days could C alone have finished the whole job? 
  • a)
    30 
  • b)
    15
  • c)
    45
  • d)
    24
  • e)
    54
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A and B can finish a job in 10 days while B and C can do it in 18 days...
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Most Upvoted Answer
A and B can finish a job in 10 days while B and C can do it in 18 days...
Given:
A+B = 10 days to finish the job
B+C = 18 days to finish the job

Let's assume the whole job requires x days to complete.

Working:
A+B = 10 days => (A+B)'s one day work = 1/x
B+C = 18 days => (B+C)'s one day work = 1/x

Now, let's calculate the work done by A, B, and C in the given days:
A worked for 5 days => A's work in 5 days = (1/x)*5
B worked for 10 days => B's work in 10 days = (1/x)*10
C worked for 15 days => C's work in 15 days = (1/x)*15

The remaining work that C did = 1 - (A's work in 5 days + B's work in 10 days)
= 1 - (5/x + 10/x)
= 1 - 15/x
= (x-15)/x

Total work done = A's work in 5 days + B's work in 10 days + C's work in 15 days + C's remaining work
= 5/x + 10/x + 15/x + (x-15)/x
= x/x
= 1

Therefore, we have:
5/x + 10/x + 15/x + (x-15)/x = 1

Solving this equation, we get x = 45.
Hence, C alone can finish the whole job in 45 days.
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A and B can finish a job in 10 days while B and C can do it in 18 days. A started the job, worked for 5 days then B worked for 10 days and the remaining job was finished by C in 15 days. In how many days could C alone have finished the whole job?a)30b)15c)45d)24e)54Correct answer is option 'C'. Can you explain this answer?
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