IIT JEE , AIEEE Forum - Mathematics , Algebra - time- work

toshi

24 men can do a piece of work in 16 days . 32 women can do the same in 24 days.16 men and 16 women started working and worked for 12 days .how many more men are added to complete the remaing work in 2 days?

please help! reply as soon as possible!

aysh

24 men can do a piece of work in 16 days.

Thus, one man can do 1/(24x16) of the work in one day.

Similarly, a woman can do 1/(32x24) of the work in one day.

Therefore,

16 men & 16 women can do 16/(24x16) + 16/(32x24) of the work in one day.

Working for 12 days, they can do

12[16/(24x16) + 16/(32x24)] = 3/4 of the work.

Work still to be done=1/4 of the original work.

Let the no. of additional men required be x.

Then,

work done by the people in 2 days=2(x+16)/(24x16) + (16x2)/(32x24)=1/4.

x=24.

Thus, required no. of additional men=24.

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iitkgp_bipin

1 man in 1 day can perform 1/(24x16) work.
1 woman in 1 day can perform 1/(32x24) work.

Hence in 12 days 16 men and 16 women perform 12{16/(24x16) + 16/(32x24)} = 3/4 work

Let additional men required be x.
In remaining 2 days 1/4 amount of work is to be done.

Hence 2{(16+x)/(24x16) + 16/(32x24)} = 1/4

x = 24 additional men required.

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