Question

47. 18 men can complete a piece of work in 24
days and 12 women can complete the same piece of work in 32 days. 18 men start working and after few days, 4 men leave the job and 8 women join. if the remaining work is completed in 15 15/23 days, after how many days did the four men leave the job.
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Answer 1

Solution :

18 men can complete a piece of work in 24 days and 12 women can complete the same piece of work in 32 days.

So , time taken by one man to complete the entire work :

=> 18 × 24 days

=> 432 days.

Time taken by one women to complete the same work :

=> 12 × 32 days

=> 384 days .

So , ratio of work done :

Man : Women - 432 : 384

=>8 : 9

So , 9 Men = 8 women.

Now , is is given that , 18 men start working.

They will complete the work in 24 days .

Now , within that 24 days period, 4 men leave.

Suppose that they leave after x days

Work done till x days :

=> 18x

Now , 14 men and 8 women are left .

Work done in 15 15/23 days :

=> 15 × 23 + 15/23

=> 360/23 days

Work done in these number of days : 360

So , the entire thing sums up to :

18 x + 360 = 18 × 24

=> 18x + 360 = 432

=> 18 x = 72

=> x = 4 days .

Hence , after 4 days from the start of the work , the 4 men left the job .

This is the required answer .

_________________________________

Answer 2

$\huge{\boxed{\bold{Question}}}$18 men can complete a piece of work in 24

days and 12 women can complete the same piece of work in 32 days. 18 men start working and after few days, 4 men leave the job and 8 women join. if the remaining work is completed in 15 15/23 days, after how many days did the four men leave the job.

Answer.

Given ;

=18 men can complete word in 24 Days.

=Total work =18*24 Man days

=432 Man Days.

12 men can complete the same piece of work in 32 days.

=Total work =18*24 Man days =432 Man days

12 men can complete the same piece of work in 32 days .

=Total work =12&32 Women Days .18*24 Man days =12*32 Woman Days

=9Men =8 woman

Let saman work of (d) days and 4men leave.

Work Done =18d Man days .

Now men =18-4=14& woman joined who are equal to 9 man

=14+9 =23 Men available.

Work done 15 15/23 Days (360/23 days)=23(360/23)=360 Man days .

18d +360=18*24

d+20=24

d=4

Hence after 4days 4 men leave

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