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A and B working separately can do a piece of work in 45 and 40 days respectively. They began the work together, but A leaves after some days and B finished the remaining work in 23 days. After how many days did A leave?
1. 6 days
2. 9 days
3. 12 days
4. 8 days

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Best answer
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".

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