Multiple choice

P, Q and R can do a piece of work in 12, 16 and 24 days, respectively. They started the work together, but P left after working for 3 days and Q left 3 days before the completion of work. In how many days was the total work completed?

  1. 6 days

  2. 8 days

  3. 12 days

  4. 9 days

  5. 11 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let total days be x. P worked 3 days (3/12 work). Q worked (x-3) days. R worked x days. Equation: 3/12 + (x-3)/16 + x/24 = 1. Multiplying by 48: 12 + 3(x-3) + 2x = 48, so 12 + 3x - 9 + 2x = 48, 5x = 45, x = 9.

AI explanation

Using the LCM method, let the total work be 48 units, making the rates of P, Q, and R equal to 4, 3, and 2 units per day respectively. Let the total time to complete the work be x days; P works for 3 days, Q works for x - 3 days, and R works for x days. The equation is (4 * 3) + 3(x - 3) + 2x = 48, which simplifies to 12 + 3x - 9 + 2x = 48. Solving 5x + 3 = 48 gives x = 9 days. The result is 9 days.

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