2026 · Q9
Eight men and 24 women can finish a piece of work in one day while 12 men and 18 women can also finish it in one day. What is the time taken by 24 men and 72 women to finish the work?
Elementary MathematicsTime and Work
- A1/3 of a day
- B2/3 of a day
- C3 days
- D9/2 days
Explanation
Let a man do m and a woman do w of the work per day: 8m+24w=1 and 12m+18w=1. Subtracting gives 4m=6w, i.e. m=1.5w, and substituting back yields 36w=1, so w=1/36 and m=1/24. Then 24 men and 72 women complete 24/24+72/36=3 works per day, so the job takes 1/3 of a day, option A.