The digging work of the DMRC on the Adohini-Andheriamore stretch requi

Question

The digging work of the DMRC on the Adohini-Andheriamore stretch requires Twenty-four men to complete the work in sixteen days. As a part of the task if DMRC were to hire Thirty-two women, they can complete the same work in twenty-four days. Sixteen men and sixteen women started working and worked for twelve days. Due to time bound schedule the work had to be completed in remaining 2 days, for which how many more men are to be employed?

A. 48
B. 36
C. 24
D. 16
E. 15

A. 48
B. 36
C. 24
D. 16
E. 15

CrackverbalGMAT · Answer

Completion of work = 1

Work done by 24 men in 16 days = 1 (Since work is completed)

Work done by 1 man in 1 day =  \frac{1}{24*16}

Work done by 32 women in 24 days = 1

Work done by 1 woman in 1 day =  \frac{1}{24*32}

So the Ratio of work = 2 : 1 or 2 women does the work of 1 man

Work done by 16 men in 12 days =  \frac{16 * 12}{24*16} = \frac{1}{2}

Work done by 16 women in 12 days =  \frac{16 * 12}{24*32} = \frac{1}{4}

Work Remaining =  1 - \frac{1}{2} - \frac{1}{4} = \frac{1}{4}

This work needs to be completed in 2 days. So work done per day =  \frac{1}{8}

\frac{1}{24*16}  is the work done by 1 man per day

To do  \frac{1}{8} th of the work, the number of men =  \frac{1 * \frac{1}{8}}{\frac{1}{24*16}} = \frac{24 * 16}{8} = 48  men

We already have 16 men + 16 women. 16 women = 8 men (as 2 women does the work of 1 man)

Therefore Extra men required = 48 - 16 - 8 = 24

Option C

Arun Kumar

WheatyPie · Answer

Choose a value for the total work that will be nicely divisible by the work done by the men ( 24*R_m*16 ) and the work done by the women ( 32*R_w*24 ), where  R_m  is the rate of 1 man, and  R_w  is the rate of 1 woman.
=> Choose the total work to be  W_t=32*24

Find the rate of 1 man:
=>  24*R_m*16=W_t 
=>  R_m=\frac{32*24}{24*16} 
=>  R_m=2

Find the rate of 1 woman:
=>  32*R_w*24=W_t 
=>  R_w=\frac{32*24}{32*24} 
=>  R_w=1

Find the work done by 16 men and 16 women in 12 days:
=>  W_{12 days}=16*R_m*12+16*R_w*12 
=>  W_{12 days}=(16*2+16*1)*12 
=>  W_{12 days}=48*12  ... or  24*24

The amount of work that remains to be done is then:
=>  W_{remaining}=W_t-W_{12 days}=32*24-24*24 
=>  W_{remaining}=8*24

This work will be done by the 16 men and 16 women who were already working, plus an additional number of men (let's call them x), over 2 days.

This work will be done by  16+x  men and  16  women. Since  R_m=2 , we get:
=>  W_{remaining}=Rate*Time 
=>  8*24= *2 
=>  4*24=(16+x)*2+16*1 
=>  x=24

Answer C.

WheatyPie · Answer

Hi Arun, you neglected to take into account the fact that we're looking for the  additional  men hired after the original 16 men and 16 women.

CrackverbalGMAT · Answer

Thank you. have edited the same.

abhinavsodha800 · Answer

Hi wheaty pie,

i tried this way but not getting the answer :

24 M * 16 D = Total Work or W 
32W * 24D = 24 M * 16 D this implies that 1M = 2W

Now work done by 16 m and 16 w is (16 M + 16 W ) * 12d or 24M * 12 d

so remaining work is 24 M * 16 D - 24 M * 12 D = 192 M D

After this i am not able to proceed ? is my approach correct

DinoPen · Answer

I did it this way... Is this approach correct?  CrackVerbalGMAT

Rate of men: 1 / (24*16)
Rate of women: 1 / (32*24)

Find the additional # of men required to finish work in 12 days:
16 men + 16 women in 12 days =
x additional men / (24*16) + 1/24 + 1/48 = 1/12
3x / (24*16) + 72 / 1152 = 1/ 12
3x + 72 = 96
3x = 24

Hence C.

CrackverbalGMAT · Answer

Hi. The approach is correct

CEdward · Answer

This is a difficult problem.

Arun, can you explain this last step here: To do 1818th of the work, the number of men = 1∗18/1/(24∗16) = (24∗16)/8=48 men?

Why does dividing the remaining work by the amount of work done by a man per day get you the total number of men 48?

Also, how did you conclude that the ratio of work b/w men and women is 1:2 up above?

CrackverbalGMAT · Answer

Hi CEdward.

First the ratio.

Work done by Men in 1 day : Work done by women in 1 day =  \frac{1}{24*16}  :  \frac{1}{24*32}  =  \frac{1}{16} : \frac{1}{32} = 2 : 1

Now the remaining work. It is simple unitary method

\frac{1}{24*16}  work done by 1 man in 1 day

Therefore to do  \frac{1}{8}  of the work ... ? men

=  \frac{\frac{1}{8}*1}{\frac{1}{24*16}}  = 48

Hope this helps.

Arun Kumar

maniknct · Answer

24mX16=1(assuming working speed of man is m) 
32wx24=1(assuming working speed of woman is w)
from above: m:w=2:1,
let total work is 48 unit, in twelve days (16m+16w or 8m=24m) 24 man can complete 36 unite, for completing remaining (6+6=12) 12 unit, we need 24m+extra24m to complete in 2 days.
So Ans:C

The digging work of the DMRC on the Adohini-Andheriamore stretch requi

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