Multiple choice

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

  1. 30 days

  2. 35 days

  3. 40 days

  4. 45 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's work in (3/4)t time = (1/2) of B's work in t time → A's rate : B's rate = (1/2)/(3/4) = 2/3. Together in 18 days: (2/3 + 1) × B's work = 18 days → (5/3)B = 18 → B = 18 × 3/5 = 54/5 = 10.8 days for full work. This is wrong; recalculate: If B's rate = 1 work per x days, A's rate = (1/2)/(3/4x) = 2/3x. Combined: 1/x + 2/3x = 18 days → 5/3x = 18 → x = 30 days. B takes 30 days alone.

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