Question

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A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was

1. 9
2. 10
3. 11
4.12

Answer 1

hey , your answer is --

Solution:
Option(D) is correct

(A+B)'s 1 day's work = 1/45+1/40=17/360

Work done by B in 23 days = 1×23/40=2340

Remaining work = 1−23/40=17/40

Now,  17/360work was done by (A+B) in 1 day.

17/40 work was done by (A+B) in 1×360/17×17/40=9 days1×360/17×17/40=9 days

Therefore, A left after 9 days.

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Answer 2

Given that A can do a work in 45 days.

A's 1-day work = 1/45  ----- (1)

Given that B can do a work in 40 days.

B's 1-day work = 1/40  ---- (2)

Now,

(A + B)'s 1-day work = 1/45 + 1/40

                                  $= \frac{1 * 8 + 1 * 9}{360}$

                                  $= \frac{17}{360}$




Given that B completed the remaining work in 23 days = 1/40 * 23

                                                                                              = 23/40.


Now,

Remaining work = 1 - 23/40

                            = 17/40.



Now,


If, 17/360 work was done was done in 1-day.

Then 17/40 work can be done in = 360/17 * 17/40

                                                       = 9 days.



Therefore the number of days after which A left the work was = 9 days.


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