Multiple choice

P can do a piece of work in $9$ days. Q is $50\%$ more efficient than P. The number of days it takes Q to do the same piece of work is __________.

  1. $\displaystyle 13\frac{1}{2}$
  2. $\displaystyle 4\frac{1}{2}$
  3. $6$
  4. $3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P's rate = 1/9 work/day. Q is 50% more efficient, so Q's rate = 1.5 * (1/9) = 3/2 * 1/9 = 1/6 work/day. Time taken by Q = 1 / (1/6) = 6 days.

AI explanation

Efficiency and time are inversely proportional, so the ratio of P's time to Q's time is the inverse of their efficiency ratio. If Q is 50 percent more efficient than P, Q's efficiency is 150 percent of P's, making the efficiency ratio 3 to 2. Therefore, the time ratio of P to Q is 2 to 3, meaning Q's time is P's time multiplied by 2/3. Since P takes 9 days, Q takes 9 multiplied by 2/3, which equals 6 days.

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