CDS 2026 (I) Elementary Mathematics, question 14

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

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Q14

X can do a piece of work in 4 days and Y can do the same piece of work in 6 days. Which of the following statements is/are correct ?

I. If X and Y work alternately starting with X, then the piece of work will be finished on the fifth day.

II. If X and Y work alternately starting with Y, then the piece of work will be finished in less than 5 days.

Select the answer using the code given below :

  1. (a) I onlyCorrect answer
  2. (b) II only
  3. (c) Both I and II
  4. (d) Neither I nor II

Solution.

Answer: (a) I only

  1. In two days, X and Y together complete 1/4+1/6=5/121/4 + 1/6 = 5/12 of the work.
  2. After four alternating days, 5/65/6 is complete regardless of who starts.
  3. If X starts, the remaining 1/61/6 takes (1/6)/(1/4)=2/3(1/6)/(1/4) = 2/3 of day 5: total 4⅔ days.
  4. If Y starts, Y needs the whole fifth day: total 5 days, not less than 5.