Time and work questions, with answers

The questions, with answers

1. 1.What is the one idea behind every time and work question?

   Work rate. If A finishes a job in 12 days, A does 1/12 of it per day; rates add when people work together, and time is work divided by rate. To avoid fractions, take the total work as the LCM of the given times and think in units: a 12-day job and an 18-day job become 36 units, so A does 3 units a day and B does 2. Every question on this page is that idea plus one twist — someone leaves, someone is faster, a pipe empties instead of fills — and the twist is always about what happens to the rate or to the work remaining.

2. 2.If A can do a job in 10 days and B in 15 days, how long do they take together?

   Add the rates. A does 1/10 per day, B does 1/15, together 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 per day, so the job takes 6 days. In LCM units: total work 30, A does 3 a day, B does 2, together 5 a day, 30 / 5 = 6. The standard mistake is averaging the days, or answering 25; the together time is always less than the faster worker's time alone. Formula for two workers: ab / (a + b) days, here 150 / 25 = 6.

3. 3.How do you handle a problem where one person leaves before the work is finished?

   Compute how much work was done while both were present, subtract it from the total, and let the remaining worker finish the rest at their own rate. Example: A can do a job in 20 days and B in 30, they start together, and A leaves after 5 days. Total work 60 units; A does 3 a day, B 2. In 5 days together they finish 25 units, leaving 35. B alone at 2 a day needs 17.5 more days, so the job takes 22.5 days in all. Always answer the question actually asked — "how many more days" (17.5) versus "total days" (22.5) are both common.

4. 4.How do men-days problems work?

   Total work is measured in man-days (or man-hours): people × days × hours per day, divided by work done. Hold that product constant across the two situations — M1 × D1 × H1 / W1 = M2 × D2 × H2 / W2 — and solve for the unknown. Example: 12 workers finish a job in 8 days working 6 hours a day; how many days do 16 workers take at 9 hours a day? 12 × 8 × 6 = 576 worker-hours; 576 / (16 × 9) = 4 days. More workers or longer days mean fewer days (inverse); more work means more days (direct). Check the direction before you compute, because that is where the sign of the mistake comes from.

5. 5.What does "A is twice as efficient as B" mean for the calculation?

   Efficiency is rate, so twice as efficient means twice the rate and half the time. If B's rate is x per day, A's is 2x. Example: A is twice as efficient as B, and together they finish a job in 8 days. Together they do 3x per day, so 3x × 8 = 1 job, x = 1/24: B alone takes 24 days and A alone takes 12. Efficiency ratios also arrive as "A does the work in 60% of the time B takes": the times are in ratio 3 : 5, so the rates are in ratio 5 : 3. Times and rates are always inverse to each other — write the ratio the question gives, then flip it if you need the other one.

6. 6.How do pipes and cisterns questions work with an outlet pipe?

   Exactly like workers, except an emptying pipe has a negative rate. A filler that fills the tank in 4 hours contributes +1/4 per hour; a drain that empties it in 12 hours contributes -1/12. Both open: 1/4 - 1/12 = 3/12 - 1/12 = 2/12 = 1/6, so the tank fills in 6 hours. If the drain were faster than the filler the net rate would be negative and the tank would never fill from empty — a trap the question sometimes sets on purpose. When a leak makes a known pipe take longer, the difference between the two rates is the leak's rate: fills in 6 hours alone, 8 with the leak, so the leak empties at 1/6 - 1/8 = 1/24, a full tank in 24 hours.

7. 7.How are wages split when people finish a job together?

   In proportion to the work each did, which for the same number of days is in proportion to their rates. A can finish a job in 6 days and B in 8; they complete it together and are paid Rs 700. Rates 1/6 and 1/8 are in the ratio 8 : 6 = 4 : 3, so A gets 400 and B gets 300. If the two worked different numbers of days, weight each rate by its days first — the split follows work done, never days present alone. The same logic settles the "C was hired to help" variant: C's share is whatever work remained after A and B's contributions, which is found by the together-and-remaining method.

8. 8.How do you solve problems that give the pairs A+B, B+C and A+C?

   Add all three pair rates: that counts each person twice, so halving the sum gives the rate of all three together, and subtracting a pair's rate from it isolates the third person. Example: A and B can finish in 10 days, B and C in 12, A and C in 15. Pair rates: 1/10 + 1/12 + 1/15 = 6/60 + 5/60 + 4/60 = 15/60 = 1/4. Halve it: all three together do 1/8 per day, so 8 days together. A alone is (A+B+C) - (B+C) = 1/8 - 1/12 = 3/24 - 2/24 = 1/24, so 24 days. B alone is 1/8 - 1/15 = 7/120, about 17.1 days; C alone is 1/8 - 1/10 = 1/40, 40 days.

How the diagnostic asks it

One question from the Aptitude bank, exactly as a sitting would show it. The bank has 4 on time and work and 60 across Aptitude.