Work problem.

[AndyB]

Hi All,

Please help me in understanding the concept behind this quesiton.

Q)45 men can complete a work in 16 days.Six days after they started working, 25 more men joined them.How many days will they now take to complete the remaining work..???
Ans)6 days

Explanation-
M1xD1/W1=M2xD2/W2
45x6/(6/16)=75xdx(1-(6/16))
=6

I understand the calculation part, I have few questions.

1)What is this formula - M1xD1/Wi=M2xD2/W2..???
2)How come work done by 45 men in 6/16 days equal to the remaining work done by 75 men in 1-6/16 days...??(Seriously confused at this point)

I just dont want blindly to use the formula.

[Bharat]

Answer 6 days (with a correction in the problem statement: 30 persons must have joined the team later rather than 25)
Approach:
45 Men > 1 Work > 16 days
1 Man > 1 Work > 16*45 days

Work completed by 45 men in 6 days = 6/16 work
remaining work after 6 days: 1 - (6/16) = 10/16 work
new work force: 45 + 30 = 75

75 Men > 10/16 work > (1 man's workdays/75)* (remaining work)
= (16*45/75)*(10/16) = 6 days

PS: if we calculate with addition of 25 men then answer is a fractional value: 45/7

Let me know in case of any questions. Thanks.

[diebeatsthegmat]

Hi All,

Please help me in understanding the concept behind this quesiton.

Q)45 men can complete a work in 16 days.Six days after they started working, 25 more men joined them.How many days will they now take to complete the remaining work..???
Ans)6 days

Explanation-
M1xD1/W1=M2xD2/W2
45x6/(6/16)=75xdx(1-(6/16))
=6

I understand the calculation part, I have few questions.

1)What is this formula - M1xD1/Wi=M2xD2/W2..???
2)How come work done by 45 men in 6/16 days equal to the remaining work done by 75 men in 1-6/16 days...??(Seriously confused at this point)

I just dont want blindly to use the formula.

heyyyy
how come it is 6 days while its only 25 more workers?

[goyalsau]

Answer 6 days (with a correction in the problem statement: 30 persons must have joined the team later rather than 25)
Approach:
45 Men > 1 Work > 16 days
1 Man > 1 Work > 16*45 days

Work completed by 45 men in 6 days = 6/16 work
remaining work after 6 days: 1 - (6/16) = 10/16 work
new work force: 45 + 30 = 75

75 Men > 10/16 work > (1 man's workdays/75)* (remaining work)
= (16*45/75)*(10/16) = 6 days

PS: if we calculate with addition of 25 men then answer is a fractional value: 45/7

Let me know in case of any questions. Thanks.

You are right it should be 30,
People just don't check , its really sad,

[AndyB]

Hi All,

Its not 30 persons to be added, It is 25 persons.
Previously there was a typo, I have put the formula right but the calculation done by me was wrong.
Really soory for this.

Problem Explanation:

M1xD1/W1=M2xD2/W2
45x6/(6/16)=75xd/(1-(6/16))
(45 x6x16)/6=(75xdx16)/10
45x16=15x8xd
d=6

My concern is really what i have said in my post.

[goyalsau]

Hi All,

Its not 30 persons to be added, It is 25 persons.
Previously there was a typo, I have put the formula right but the calculation done by me was wrong.
Really soory for this.

Problem Explanation:

M1xD1/W1=M2xD2/W2
45x6/(6/16)=75xd/(1-(6/16)) ( 45+ 25 is not 75 , as i know )
(45 x6x16)/6=(75xdx16)/10
45x16=15x8xd
d=6

My concern is really what i have said in my post.

Dear i must say, you questions has really made me crazy, Sadly i was working on Work problems ,,, as i studied the concept just few days back, I was really worried how am i wrong..............

What to say, Guys,,,,,,,,

[AndyB]

Sorry Guys,

U were correct, after working on this work rate problems.
Looks like I have gone out of my mind.
Yes it should me 30 persons.

But could anyone shed some light on the formula and how to use it.

Once again sorry guys for causing trouble.

[GMATGuruNY]

Hi All,

Please help me in understanding the concept behind this quesiton.

Q)45 men can complete a work in 16 days.Six days after they started working, 30 more men joined them.How many days will they now take to complete the remaining work..???
Ans)6 days

Explanation-
M1xD1/W1=M2xD2/W2
45x6/(6/16)=75xdx(1-(6/16))
=6

I understand the calculation part, I have few questions.

1)What is this formula - M1xD1/Wi=M2xD2/W2..???
2)How come work done by 45 men in 6/16 days equal to the remaining work done by 75 men in 1-6/16 days...??(Seriously confused at this point)

I just dont want blindly to use the formula.

We could plug in a value for how much work is being done by each man.

Plug in that each man completes 2 unit/day.
Thus, 45 men complete 45*2 = 90 units/day.
Over 16 days, 16*90= 1440 units are completed. This is the value of the job.
In 6 days, 45 men complete 6*90 = 540 units.
1440-540 = 900 units left.
When 30 men join, total men = 45+30 = 75 men.
Rate for 75 men = 75*2 = 150/day.
Time for 75 men = w/r = 900/150 = 6 days.

[AndyB]

Thank You Mitch.
It was very simple but I struggled a lot to understand when i used the formula.