Multiple choice

Arun can do half as much work as Bipul in three-fourth of the time. If they take 21 days to complete the work together, then how much time shall Bipul take to do the work?

  1. 32 days

  2. 35 days

  3. 37 days

  4. 39 days

  5. 42 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Arun takes 3/4 time of Bipul to do half work. So Arun takes 3/2 time of Bipul to do full work. Let Bipul take x days, then Arun takes 1.5x days. 1/x + 1/1.5x = 1/21. (1.5 + 1) / 1.5x = 1/21. 2.5 / 1.5x = 1/21. 5 / 3x = 1/21. 3x = 105, so x = 35.

AI explanation

Let Bipul's work be W, so Arun does half that work, which is W/2. Arun takes three-fourth of Bipul's time to do W/2, so if Bipul's total time is T, Arun's total time to do W would be 2 * (3T/4), which is 3T/2. Their combined 1-day work is 1/T + 2/(3T) = 5/(3T), which equals 1/21 since they finish in 21 days. Solving 5/(3T) = 1/21 gives 3T = 105, so Bipul takes 35 days.

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