Multiple choice

Passage

Directions: Study the following information carefully and answer the given question. The data below represents the number of people required for various assignments to be completed in various days. Assignment Situation 1 Situation 2 Number of Employees Days Required Number of Employees Days Required X (p + 10) p (p + 20) (p – 6) Y (q + 5) 60 15 (q + 80) Z 125 r 2 20 s 2

If (p - 10) employees are working on assignment X, then how many days will it take to complete 1/12th part of assignment X?

  1. 4

  2. 6

  3. 5

  4. 8

  5. 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the same assignment, employees multiplied by days is constant: (p + 10)p = (p + 20)(p - 6), which gives p = 30. The full work is 40 × 30 = 1,200 employee-days, so 1/12 of it requires 100 employee-days, or 100/20 = 5 days.

AI explanation

First, use assignment X to find the value of p by equating the total work in both situations, which gives (p + 10) * p = (p + 20) * (p - 6). Expanding and simplifying this equation yields p^2 + 10p = p^2 + 14p - 120, so 4p = 120 and p = 30. The total work for assignment X is then (30 + 10) * 30 = 1200 units. The given workforce is p - 10 = 20 employees, and one twelfth of the work is 1200 / 12 = 100 units, so dividing 100 units by 20 employees gives exactly 5 days. 5.

Keep practicing — related questions