Multiple choice

A takes 50% more time than B who can complete a piece of work in 20 days. Both A and B started working together. After 6 days, A left the work and B did half of the pending work alone. Then, A joined B and they completed rest of the work together. In how many days was the whole work completed?

  1. 8 days

  2. 9 days

  3. 11 days

  4. 14 days

  5. 16 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

B takes 20 days, A takes 30 days. Work rates: B=1/20, A=1/30. Together: 1/20+1/30 = 5/60 = 1/12. In 6 days, they do 6/12 = 1/2 work. Remaining 1/2. B does half of remaining (1/4) in 5 days. Remaining 1/4. A+B do 1/4 at rate 1/12 in 3 days. Total = 6+5+3 = 14 days.

AI explanation

B takes 20 days, so A takes 1.5 * 20 = 30 days. Their combined 6-day work equals 6 * (1/20 + 1/30) = 1/2 of the job, leaving 1/2 of the job pending. B does half of this pending work, which is 1/4 of the total job, taking (1/4) / (1/20) = 5 days. The remaining 1/4 of the job is done by A and B together at a rate of 1/12 per day, taking (1/4) / (1/12) = 3 days. The total time is 6 + 5 + 3 = 14 days.

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