CDS 2026 (I) Elementary Mathematics, question 9

Topic: Arithmetic (percentage, ratio, interest, time and work, speed)

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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 ?

  1. (a) 13\frac{1}{3} of a dayCorrect answer
  2. (b) 23\frac{2}{3} of a day
  3. (c) 33 days
  4. (d) 92\frac{9}{2} days

Solution.

Answer: (a) 13\frac{1}{3} of a day

  1. The required team, 24 men and 72 women, is exactly three times the team of 8 men and 24 women that completes the work in one day.
  2. With the same individual work rates, its combined rate is three times as large.
  3. Shortcut: The second team equation is unnecessary because the required team is a direct multiple of the first.