Multiple choice

$A$ is thrice as good a work man as $B$ and takes $60$ days less than $B$ for doing a job. Find the time in which they can do it together.

  1. $15\dfrac{9}{3}$
  2. $22\dfrac{4}{9}$
  3. $15\dfrac{7}{4}$
  4. $22\dfrac{1}{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let B take x days, A takes x/3 days. x - x/3 = 60 => 2x/3 = 60 => x = 90. A takes 30 days, B takes 90 days. Together: (1/30 + 1/90)^-1 = (4/90)^-1 = 90/4 = 22.5 days.

AI explanation

Since A is thrice as good as B, the ratio of their times taken is 1:3, so if B takes 3x days, A takes x days. The difference is 2x = 60 days, meaning x = 30, so A takes 30 days and B takes 90 days. Their combined one-day work is 1/30 + 1/90 = 4/90 = 2/45. Using the formula for combined work, they complete the job in 45/2 days, which equals 22 and 1/2 days.

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