Aptitude Discussion

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 |

**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.**

**Aditya**

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**WIZ**

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Answer is correct but you have not done the calculations correctly

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.