Time and Work Questions

Multiple choice
  1. $\displaystyle\frac{x}{100y(1-z)}$days
  2. $\displaystyle\frac{100yz}{x}$days
  3. $\displaystyle\frac{100x}{y(100-z)}$days
  4. $\displaystyle\frac{100}{y(z-1)}$days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The company produces y goods daily, but z% are unfit, so effective production is y * (1 - z/100) = y * (100 - z) / 100. To produce x goods, the time required is x / (effective production) = x / (y * (100 - z) / 100) = 100x / (y * (100 - z)).

Multiple choice
  1. $\displaystyle 13\frac{1}{3}$ days
  2. $15$ days
  3. $20$ days
  4. $30$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A = 0.5B. C = 0.5(A+B) = 0.5(1.5B) = 0.75B. C does work in 40 days, so total work = 40 * 0.75B = 30B. A+B+C = 0.5B + B + 0.75B = 2.25B. Time = 30B / 2.25B = 30 / 2.25 = 13.33 days.

Multiple choice
  1. $40$%
  2. $25$%
  3. $30$%
  4. $27$%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate = (3/4)/18 = 1/24 per day. B's rate = (2/3)/12 = 1/18 per day. C's rate = 0.6/24 = 1/40 per day. Work done = 4*(1/24) + 6*(1/18) + 8*(1/40) = 1/6 + 1/3 + 1/5 = (5+10+6)/30 = 21/30 = 0.7. Pending work = 1 - 0.7 = 0.3 or 30%.

Multiple choice
  1. $22$
  2. $20$
  3. $18$
  4. $16$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be the original number of workers. The total work is 25x. After 6 workers leave, the remaining (x-6) workers finish in 40 days, so 40(x-6) = 25x. Solving 40x - 240 = 25x gives 15x = 240, so x = 16.

Multiple choice
  1. ${ 7 }_{ 4 }^{ 3 }$
  2. ${ 8 }_{ 5 }^{ 4 }$
  3. ${ 9 }_{ 8 }^{ 3 }$
  4. 10 days

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A does 1/3 in 5 days, so A takes 15 days for the whole work. B does 2/5 in 10 days, so B takes 25 days for the whole work. Combined rate = 1/15 + 1/25 = (5+3)/75 = 8/75. Time = 75/8 = 9 and 3/8 days.

Multiple choice
  1. $15$ days
  2. $14$ days
  3. $13$ days
  4. $10$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A does 5/40 = 1/8 of the work. Remaining work = 7/8. B does 7/8 in 21 days, so B's rate is (7/8) / 21 = 1/24. Together, their rate is 1/40 + 1/24 = (3+5)/120 = 8/120 = 1/15. They take 15 days together.