Time and Work
Aptitude

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Q.

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.

24

 C.

36

 D.

16

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Solution:
Option(B) is correct

From the given data we can write that the total work is equivalent to \(24\times 16\) Man-Days. Which in turn is equivalent to \(32\times 24\) woman-Days.

Hence 1 Man-Day is equivalent to 2 Woman-Days. 

Let $x$ be the number of additional men required for the last two days’ work

Total work = \(24\times 16\)

⇒ (16 Men +16 Women) × 12-Days +(16 Men +16 Women) × 2-Days

⇒ (16 Men + 16/2 men) × 2-Days men) × 12-Days +(16 Men + 16/2 men)× 2-Days

 ⇒ 24×16=24×12+(24+x)×2

⇒ x= 24.


(3) Comment(s)


Anonymous
 ()

This answer is given wrong. Answer would be 48

Solution- 24M*16 = 32W*24

then ratio of men and women will be 2:1

then put this value in above any 1 equation to get complete work.

(24M*16) i.e. 24*2*16=768

now according to the question condition

(16M=16W)12....put value of m and w 2 and 1 respectively

(48)12=576

this is the total work done by 16 men and 16 women in 12 days

now subtract this work form complete work then the remaining would be 192.

Since 1 men complete 2 units of work in 1 day and we have to complete the work in 2 days then the no of men will be x

then the equation would be 192/2x=2

and on solving this 48 men would be answer.



Aditya
 ()

24 men can complete in 16 days, then the work done by one man in a day is 1/384 now for women, 32 women can complete in 24 days then work done by one woman in one day is 1/768.

Hence, one man and one woman together one day work is (1/384+1/768)= 1/256

Similarly work done by 16 women and 16 men together for 12 days is given by= (16*12)/256= 3/4

Hence, the remaining work after 12 days is=(1-3/4)= 1/4

Now, the remaining work have to be completed in next 2 days.

the work done by 16 men and 16 women in 2 days is 1/8.

the remaining work is=(1/4-1/8)=1/8

Now, No. of additional men required to complete the work in next 2 days is=384*1/8*1/2= 24men.



WIZ
 ()

Answer is correct but you have not done the calculations correctly