Question

Tim started a job alone and Bob joined him after a few days. The work got completed in 8 days. Tim would have required 2 more days to complete the
work alone whereas Bob could have completed the work alone in 25 days. For how many days did Bob work?

a) 3
b) 6
c) 5
d) 2​

Answer 1

I have a bagI have a bagI have a bagI have a bag

Answer 2

Solution :-

given that, tim would have required 2 more days to complete the work alone .

So,

→ Tim completed the job alone in = 8 + 2 = 10 days .

→ Bob completed the job alone in = 25 days .

then,

→ LCM of 10 and 25 = 50 units = Let total work .

now,

→ Efficiency of Tim = Total work / Total time taken = 50/10 = 5 units / day .

→ Efficiency of Bob = Total work / Total time taken = 50/25 = 2 units / day .

Let us assume that, Tim worked alone for x days .

then,

→ Tim efficiency * Time + (Tim + Bob) efficiency * Time = Total work

→ 5 * x + (5 + 2) * (8 - x) = 50

→ 5x + 7(8 - x) = 50

→ 5x + 56 - 7x = 50

→ 56 - 2x = 50

→ 2x = 56 - 50

→ 2x = 6

→ x = 3 days .

therefore,

→ Bob did worked for = 8 - 3 = 5 days (c) (Ans.)

Hence, Bob did worked for 5 days with Tim to completes the work .

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