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A and B can separately finish a piece of work in 20 days and 15 days respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in next 4 days, then the number of days in which C alone could do the work is    (SSC Sub. Ins. 2016)
  • a)
    50 days
  • b)
    30 days
  • c)
    40 days
  • d)
    60 days
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A and B can separately finish a piece of work in 20 days and 15 days r...

(A + C)'s 4 day's work  = 3/10
(A + C)'s 1 day's work  = 3/20
A's 1 day's work = 1/20

Hence C alone can finish the work in 40 days.
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Community Answer
A and B can separately finish a piece of work in 20 days and 15 days r...
Given Data:
A can finish work in 20 days
B can finish work in 15 days
A and B worked together for 6 days
B was replaced by C and the work was finished in the next 4 days

Calculations:
Let the total work be 60 units (LCM of 20 and 15)
A's work rate = 60/20 = 3 units/day
B's work rate = 60/15 = 4 units/day

Working together:
In 6 days, A and B complete (6 * (3 + 4)) = 42 units of work
Remaining work = 60 - 42 = 18 units

After B is replaced by C:
In the next 4 days, A and C complete the remaining 18 units of work
A's work in 4 days = 4 * 3 = 12 units
Remaining work for C = 18 - 12 = 6 units
C's work rate = 6/4 = 1.5 units/day

Calculation for C:
Since C's work rate is 1.5 units/day, the number of days C alone would take to complete the work = 60/1.5 = 40 days
Therefore, the number of days in which C alone could do the work is 40 days (Option C).
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A and B can separately finish a piece of work in 20 days and 15 days respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in next 4 days, then the number of days in which C alone could do the work is (SSC Sub. Ins. 2016)a)50 daysb)30 daysc)40 daysd)60 daysCorrect answer is option 'C'. Can you explain this answer?
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