Multiple choice

P does half the work what Q does in one sixth of the time. If they take 10 days to complete a work together, how much time will Q take to do it alone?

  1. 30 days

  2. 50 days

  3. 40 days

  4. 60 days

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P completes half the work Q completes in one-sixth of Q's time, so P's rate is three times Q's rate. Together their rate is four times Q's rate, and since they finish in 10 days, Q alone takes 40 days.

AI explanation

Assuming Q alone takes x days, Q's 1 day work is 1/x; since P does half the work in one-sixth the time, P takes one-third the time Q takes, so P takes x/3 days and his 1 day work is 3/x. Their combined 1 day work is 1/x + 3/x = 4/x, and working together they finish the job in 10 days, which means their combined 1 day work is also 1/10. Equating these gives 4/x = 1/10, so x equals 40 days.

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