Multiple choice

P can do a piece of work in 21 days and Q in 28 days. Together they start the work and Q leaves after 4 days. In how many days can P alone do the remaining work?

  1. 20 days

  2. 12 days

  3. 17 days

  4. 14 days

  5. 6 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

P's rate = 1/21, Q's rate = 1/28. Together in 4 days: 4 * (1/21 + 1/28) = 4 * (4+3)/84 = 4 * 7/84 = 4/12 = 1/3. Remaining work = 2/3. P alone takes: (2/3) / (1/21) = (2/3) * 21 = 14 days.

AI explanation

Let the total work be the least common multiple of 21 and 28, which is 84 units, making the daily work of P equal to 4 units and the daily work of Q equal to 3 units. Working together for 4 days, they complete 7 units per day for a total of 28 units, leaving 56 units of work remaining. Since P works alone at a rate of 4 units per day, the time required to finish the remaining work is 56 divided by 4, which equals 14 days.

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