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A, B and C can complete a work in 10, 12 and 15 days respectively. All three of them start together but after 3 days A leaves the job and B left the job 2 days before the work was completed. C completed the remaining work alone. In how many days was the total work completed? 
  • a)
    25/9 days 
  • b)
    52/9 days 
  • c)
    26/9 days 
  • d)
    53/9 days 
Correct answer is option 'B'. Can you explain this answer?
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A, B and C can complete a work in 10, 12 and 15 days respectively. All...
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A, B and C can complete a work in 10, 12 and 15 days respectively. All...
Given:
A can complete work in 10 days
B can complete work in 12 days
C can complete work in 15 days

Approach:
Let's assume the total work is equal to LCM of 10, 12 and 15 i.e. 60 units.
Using the formula, Time = (Work)/(Rate), we can find the rate of each person.
Let's assume they work for 'D' days together.

Calculation:
The rate of A = 6 units/day (60 units/10 days)
The rate of B = 5 units/day (60 units/12 days)
The rate of C = 4 units/day (60 units/15 days)

Let's assume they work together for 'D' days. Therefore, the work completed by them in 'D' days will be:
(6+5+4)D = 15D units

After 3 days, A left the job. Therefore, the work completed in 3 days will be:
6*3 = 18 units

After 3 days, the remaining work is (60-18) = 42 units.

Assuming the work is completed in 'T' days (after A left the job), we can write the equation as:
5(T-2) + 4T = 42

Solving this equation, we get T= 16/3 days

Therefore, the total time taken to complete the work will be:
3 + 16/3 = 25/3 days

Converting into mixed fraction, we get 8 1/3 days.

Therefore, the correct option is (b) 52/9 days.
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A, B and C can complete a work in 10, 12 and 15 days respectively. All three of them start together but after 3 days A leaves the job and B left the job 2 days before the work was completed. C completed the remaining work alone. In how many days was the total work completed?a)25/9 daysb)52/9 daysc)26/9 daysd)53/9 daysCorrect answer is option 'B'. Can you explain this answer?
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