Multiple choice

Passage

Directions: The question below contains a statement followed by Quantity I and Quantity II. Find both the quantities to determine the relationship among them and mark your answer accordingly.

Govind and Rahul can do a piece of work in 20 days, Rahul and Pankaj can complete the same work in 30 days, and Pankaj and Govind can complete half of that work in 25 days. Quantity I: Number of days required to complete the work by Govind alone Quantity II: Number of days required to complete the work by Pankaj alone

  1. Quantity I ≥ Quantity II

  2. Quantity I ≤ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I > Quantity II

  5. Quantity I = Quantity II, or the relationship cannot be established from the information given.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

1/G + 1/R = 1/20, 1/R + 1/P = 1/30, 1/P + 1/G = 1/50 (since half work in 25 days). Sum: 2(1/G + 1/R + 1/P) = 1/20 + 1/30 + 1/50 = (15+10+6)/300 = 31/300. 1/G + 1/R + 1/P = 31/600. 1/P = 31/600 - 1/20 = (31-30)/600 = 1/600 => P=600. 1/G = 31/600 - 1/30 = (31-20)/600 = 11/600 => G=54.54. G < P.

AI explanation

Let the one day work of Govind, Rahul, and Pankaj be g, r, and p. Given g plus r equals 1 by 20 and r plus p equals 1 by 30, while p plus g equals 1 by 50 because they complete half the work in 25 days. Adding all three equations gives 2 times the sum of g, r, and p equals 17 by 300, so their combined one day work is 17 by 600. Subtracting the sum of g and p from this total gives Rahul's one day work as 7 by 600, so Govind's one day work is 1 by 20 minus 7 by 600, which equals 23 by 600, meaning Govind takes about 26.08 days. Pankaj's one day work is 1 by 30 minus 7 by 600, which is 13 by 600, meaning Pankaj takes about 46.15 days; therefore, Govind takes fewer days than Pankaj.

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