Correct Answer - Option 1 : 6 days
Formula used:
Total work = Number of days × Efficiency.
Concept:
The number of days and work is inversely proportional to each other.
Calculation:
As per the question,
A and B can do a piece of work in 45 and 40 days respectively.
Therefore, A's one day work will be = (1/45).
Also, B's one day work will be = (1/40).
Again as per the question,
A leaves work after some days and B finished the work in 23 days.
Let, "A" be leaving the work in "x" days.
Therefore, work done by "A" in "x" will be = (x/45) units.
Also, work done by "B" in (x + 23) days will be = (x + 23)/40.
Therefore,
⇒ (x/45) + ((x + 23)/40) = 1.
⇒ x/45 + x/40 + 23/40 = 1.
⇒ 8x + 9x + 207 = 360.
⇒ 17x + 207 = 360.
⇒ 17x = 360 - 207.
⇒ 17x = 153.
⇒ x = 153/17.
⇒ x = 9.
Hence, "A" leaves after 9 days.
Therefore, the correct answer should be "Option 2: 9d ays".