Multiple choice

Directions: Type in your answer in the input box provided below the question. A starts a certain work and after he completes exactly half the work, he leaves and B takes up the remaining work and it takes a total of 25 days for the work to be completed this way. If A and B working together can complete the work in 12 days, and A is slower than B, then find the number of days in which the work will be completed, if A alone first works on exactly one-fifth of the work, after which B alone completes the rest of the work.

  1. 21

  2. 22

  3. 23

  4. 24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A and B take 'a' and 'b' days to complete the work. 1/a + 1/b = 1/12. Given 0.5a + 0.5b = 25, so a + b = 50. Solving the system: x^2 - 50x + 600 = 0, giving roots 20 and 30. Since A is slower, A=30, B=20. For the second scenario: (1/5) * 30 + (4/5) * 20 = 6 + 16 = 22 days.

AI explanation

Let A take x days and B take y days to complete the work alone. From the conditions we have x/2 + y/2 = 25 and xy/(x + y) = 12. Multiplying the first equation by 2 gives x + y = 50, and multiplying the second equation by (x + y) gives xy = 12(x + y), so xy = 600. Solving x + y = 50 and xy = 600 gives the roots 30 and 20; since A is slower, x is 30 and y is 20. The time taken for A to complete one-fifth of the work and B to complete the rest is 30/5 + 20(4/5), which equals 6 + 16, giving a total of 22 days.

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