Multiple choice

A does half as much work as B in three-fourth of the time. If together they take $18$ days to complete the work, how much time shall B take to do it?

  1. $30$ days
  2. $35 $ days
  3. $40 $ days

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A does 1/2 work in 3/4 time. So A does 1 work in (3/4) * 2 = 3/2 time. A's rate = 2/3 of B's rate. A + B = 1/18. (2/3)B + B = 1/18. (5/3)B = 1/18. B = 3/90 = 1/30. B takes 30 days.

AI explanation

If A does half the work in 3/4 of the time, A would complete the full work in 3/2 of that time, meaning A is half as efficient as B. Let the time taken by B be y days, so the time taken by A is 1.5y days, and their one day's work is 1/y plus 2/3y, which equals 5/3y. Given that together they take 18 days, their one day's work is 1/18, so equating 5/3y to 1/18 gives 3y equals 90, making y equal to 30 days.

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