Multiple choice

The ratio of efficiency of P is to R is 7 : 4 and the ratio of number of days taken by Q is to R is 2 : 3 while working alone P takes 9 days less than R to complete the work. If Q and R started the work and left after 2 days then find the number of days taken by P to finish the remaining work?

  1. 64/7 days

  2. 8 days

  3. 32/1 days

  4. 128/7 days

  5. 7 days
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A Correct answer
Explanation

Efficiency P:R = 7:4. Days Q:R = 2:3 => Efficiency Q:R = 3:2 = 6:4. So P:Q:R = 7:6:4. Let P=7x, Q=6x, R=4x. P takes 9 days less than R: 1/4x - 1/7x = 9/W => 3/28x = 9/W => W = 84x. P takes 84x/7x = 12 days. R takes 84x/4x = 21 days. Q takes 84x/6x = 14 days. Q+R work 2 days: (1/14 + 1/21)*2 = (3+2)/42 * 2 = 10/42 = 5/21. Remaining = 16/21. P finishes in (16/21) * 12 = 192/21 = 64/7 days.

AI explanation

Using the efficiency and time relationship, if the efficiency ratio of P to R is 7:4, their time ratio is 4:7. Let R take 7x days and P take 4x days, so the difference of 3x days equals 9 days, meaning x equals 3 and R takes 21 days while P takes 12 days. Since the ratio of days for Q to R is 2:3, Q takes 14 days, making their combined daily work 1/14 plus 1/21, which equals 5/42 of the work per day. In 2 days, Q and R complete 10/42 or 5/21 of the work, leaving 16/21 of the work, which P completes in 16/21 multiplied by 12 days, giving 64/7 days.

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