Twenty-four men can complete a work in sixteen days. Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working and worked for twelve days. How many more men are to be added to complete the remaining work in 2 days?

Explanation

We are given:

24 men complete the work in 16 days → 1 man's 1-day work = 1/24×16=1/38432 women complete the work in 24 days → 1 woman's 1-day work = 1/32×24=1/768 

16 men and 16 women work for 12 days

Step 1: Work done by 16 men and 16 women in 12 days

Work done by 16 men in 1 day = 16×1/384=16/384=1/24

Work done by 16 women in 1 day = 16×1/768=16/768=1/48

Total work done in 1 day = 1/24+1/48=2/48+1/48=3/48=1/16

Total work done in 12 days = 12×1/16=12/16=¾

Step 2: Work remaining

Total work = 1

Work done = ¾

Work remaining = 1−3/4=1/4

Step 3: Additional men required

The remaining work must be completed in 2 days.

Let x be the number of additional men needed.

Work done by (16 + x) men in 1 day = (16+x)×1384(16 + x) 

Work done in 2 days = 2×(16+x)×1384=142

Solving for x:

(16+x)×2/384=¼

16+x=1/4×384/2=384/8=48

x=48−16=32

The closest option is 36 men

Related MCQs