Time and Work Questions

Multiple choice
  1. $10$ days
  2. $9$ days
  3. $8$ days
  4. $7$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A take x days and B take x+5 days. Their combined rate is 1/x + 1/(x+5) = 1/6. Solving x^2 + 5x = 6(2x + 5) leads to x^2 - 7x - 30 = 0, which factors to (x-10)(x+3) = 0. Thus, A takes 10 days.

Multiple choice
  1. $6$ days
  2. $8$ days
  3. $9$ days
  4. $5$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

B and C together complete 1/10 + 1/15 = 1/6 of the work per day. In 2 days, they complete 1/3 of the work, leaving 2/3 of the work remaining. A, who completes 1/9 of the work per day, will take (2/3) / (1/9) = 6 days to finish the remaining work.

Multiple choice

  1. $6$
  2. $8$
  3. $4$
  4. $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

12 children * 16 days = 192 child-days. 8 adults * 12 days = 96 adult-days. So 1 adult = 2 children. Total work = 96 adult-days. 16 adults work for 3 days = 48 adult-days. Remaining work = 48 adult-days. New team: 6 adults (16-10) + 4 children (2 adults) = 8 adults. Days = 48 / 8 = 6 days.

Multiple choice
  1. $10$ days
  2. $12$ days
  3. $8$ days
  4. $14$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

X does 1/8 per day, Y does 1/12, Z does 1/16. X works 2 days (2/8 = 1/4 work). Remaining is 3/4. Y works until 25% (1/4) is left for Z. So Y does 1/2 of the work. Y's time = (1/2) / (1/12) = 6 days. Z does 1/4 work in (1/4) / (1/16) = 4 days. Total time = 2 + 6 + 4 = 12 days.

Multiple choice
  1. $dx - (100 - dy)$
  2. $dx - 100y$
  3. $dx - (100 - d)y$
  4. $dx+(100-d)y$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The worker is employed for a total of 100 days. If he works for d days, he earns dx rupees. He is absent for the remaining (100 - d) days, which results in a deduction of (100 - d)y rupees. Therefore, his net earning E is given by dx - (100 - d)y.