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A and B can do a piece of work in 24 and 30 days respectively. Both started the work and worked for 6 days. Then B leaves the work and C joins and the remaining work is completed by A and C together in 11 days. Find the days in which C alone can do the work
  • a)
    80
  • b)
    100
  • c)
    120
  • d)
    130
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A and B can do a piece of work in 24 and 30 days respectively. Both st...
(1/24 + 1/30)*6 + (1/24 + 1/c)*11 = 1
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A and B can do a piece of work in 24 and 30 days respectively. Both st...
Given:

A can do a piece of work in 24 days

B can do a piece of work in 30 days

Both started the work and worked for 6 days

B leaves the work and C joins

The remaining work is completed by A and C together in 11 days

To find: Days in which C alone can do the work

Concept used:

Let the total work be 120 units (LCM of 24 and 30)

The efficiency of A = 5 units/day (120/24)

The efficiency of B = 4 units/day (120/30)

Calculation:

Total work = 120 units

Let the work done by A and B together in 6 days be x.

x = (6 × (5 + 4))

x = 54 units

Remaining work = 120 - 54 = 66 units

Let the efficiency of C be y.

Work done by A and C together in 11 days = 11 × (5 + y)

66 = 11 × (5 + y)

66 = 55 + 11y

11y = 66 - 55

y = 1 unit/day (Efficiency of C)

Therefore, C alone can do the work in 120 days.

Hence, the correct option is (c) 120.
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