Multiple choice

If $10$ men and $15$ women finish a work in $6$ days. One man alone finishes that work in $100$ days. In how many days will a women finish the work?

  1. $125$ days
  2. $150$ days
  3. $90$ days
  4. $225$ days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

1 man = 1/100 work/day. 10 men = 10/100 = 1/10 work/day. 10 men + 15 women = 1/6 work/day. 15 women = 1/6 - 1/10 = (5-3)/30 = 2/30 = 1/15 work/day. 1 woman = 1/(15*15) = 1/225 work/day. So 1 woman finishes in 225 days.

AI explanation

Using the formula for total work, Total Work equals Men times Days, one man finishes the work in 100 days so the total work is 100 man-days. Since 10 men and 15 women finish it in 6 days, the total work is also equivalent to 6 times the sum of 10 men and 15 women. Substituting the value of 1 man as 1/100th of the work, 10 men in 6 days complete 60/100 or 3/5th of the work. The remaining 2/5th of the work is done by 15 women in 6 days, meaning 15 women complete 2/5th in 6 days. Therefore, 1 woman completes 2/(5 times 15 times 6) or 1/225th of the work daily. A woman alone will finish the work in 225 days.

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