Multiple choice

Directions: In this question, two quantities are given, one as 'Quantity 1' and another as 'Quantity 2'. You have to determine the relationship between the two quantities and choose the appropriate option. Three persons X, Y and Z together can complete a piece of work in 60/11 days. The work done by Y in two days is equal to the work done by X in one day and the work done by Z in three days is equal to the work done by X in one day. Quantity 1: Time taken by Y and Z to complete the work together Quantity 2: Time taken by X and Y to complete the work together

  1. Quantity 1 > Quantity 2

  2. Quantity 1 ≥ Quantity 2

  3. Quantity 2 > Quantity 1

  4. Quantity 2 ≥ Quantity 1

  5. Quantity 1 = Quantity 2 or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let X, Y, Z be work rates. X+Y+Z = 11/60. Y = X/2, Z = X/3. X + X/2 + X/3 = 11/60 => (6+3+2)X/6 = 11/60 => 11X/6 = 11/60 => X = 1/10. Y = 1/20, Z = 1/30. Q1: Time (Y+Z) = 1 / (1/20 + 1/30) = 1 / (5/60) = 12 days. Q2: Time (X+Y) = 1 / (1/10 + 1/20) = 1 / (3/20) = 20/3 = 6.67 days. Q1 > Q2.

AI explanation

Given X, Y, and Z together complete the work in 60 by 11 days, their combined one day work is 11 by 60. Let the one day work of X, Y, and Z be x, y, and z. Given 2y equals x and 3z equals x, substituting these into the combined work equation gives x plus x by 2 plus x by 3 equals 11 by 60, which solves to x equaling 1 by 5. Thus y is 1 by 10 and z is 1 by 15. For Quantity 1, Y and Z's combined one day work is 1 by 10 plus 1 by 15, which is 1 by 6, meaning they take 6 days. For Quantity 2, X and Y's combined one day work is 1 by 5 plus 1 by 10, which is 3 by 10, meaning they take 10 by 3 days. Comparing the times, 6 days is greater than 3.33 days.

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