Exam path · Time & Work
Time and work questions give you how long each person takes alone and ask how long they take together, or the reverse. They are solved by adding rates, never by adding or averaging days. Take the total job as the LCM of the given days, convert each worker into units per day, add those, and divide — which turns the whole topic into one subtraction and one division.
Time and work is worth two marks in most banking prelims papers and appears in almost every SSC and railway paper too. It has a reputation for being slow, and it earns that reputation only when it is attacked with equations. The LCM-units method below turns the standard question into two lines of mental arithmetic, and the pipes-and-cisterns questions are the same method with one rate made negative.
Try it against the clock. Time & Work runs at 45s easy, 55s medium and 70s hard. The clock is stamped and judged on our server, so the limit you see is the deadline that is actually enforced — and it starts when you tap Start, not while the question is loading.
Generated by the same engine that mints the ComputePrep daily. Each answer is computed from the numbers printed in the question, and the walkthrough below each one is the engine's own working — not a solution written afterwards. Reload this page's live drill and you get different numbers.
Karan can complete a piece of work in 10 days.
Meera can complete the same work in 15 days.
Working together, in how many days will they finish it?
Ravi can complete a piece of work in 20 days.
Sunita can complete the same work in 30 days.
Working together, in how many days will they finish it?
Karan can complete a piece of work in 8 days.
Meera can complete the same work in 24 days.
Working together, in how many days will they finish it?
If Ravi takes 6 days and Sunita 12, call the whole job 12 units. There are no fractions after this step, which is the entire point — the fractions are what make this topic feel slow.
Ravi does 12 ÷ 6 = 2 units a day, Sunita 12 ÷ 12 = 1. These are rates, and rates are the only thing in this topic you are allowed to add.
Together they do 3 units a day, so the job takes 12 ÷ 3 = 4 days. Notice that 4 is less than either person alone — a two-person job is always faster than the faster worker, and that check alone eliminates two options.
A leak that empties the tank in 20 hours is a rate of −(work/20). Everything else is unchanged: add the rates, divide, done. A question with a leak is not a new topic, it is a minus sign.
| What the paper says | What it means |
|---|---|
| A alone: 10 days, B alone: 15 days | Rates 3 and 2 out of 30 units — together 5, so 6 days |
| A is twice as efficient as B | Rate of A = 2 × rate of B; days are in the ratio 1:2, not 2:1 |
| A and B together: 6 days, A alone: 10 | B's rate = total − A's = the subtraction that answers most of these |
| A pipe fills in 4 h, a leak empties in 12 h | Rates +3 and −1 out of 12 units — net 2, so 6 hours |
The wrong options are not random numbers. Each one is the result of a specific careless error for this topic, so picking one tells you which habit is costing you marks.
If A takes 6 days and B takes 12, together they do not take 18 days or 9. Days are not additive; rates are. Both 18 and 9 will be sitting in the options because the setter knows exactly which mistake you are about to make.
"A is twice as efficient as B" means A takes half as long, not twice as long. The sentence and the arithmetic point in opposite directions, and under a clock that is enough.
Any combined-work answer has to be smaller than the smallest individual time. If yours is not, you added days somewhere. This check costs a second and catches the majority of errors in this topic.
The LCM method. Take the total work as the LCM of the given days, convert each worker into units per day, add the rates and divide the total work by the sum. It removes every fraction from the calculation and works unchanged for pipes and cisterns.
Between 45 and 70 seconds. This drill enforces exactly that: 45 seconds on easy, 55 on medium and 70 on hard, timed on the server rather than in your browser.
Yes, mathematically. A filling pipe is a positive rate and a leak or outlet is a negative one. Add the rates the same way and divide the same way; nothing else changes.
No. The combined-time formula xy divided by x plus y is just the LCM method written out, and it only covers the two-worker case. Learning the rate method once covers every variant, including efficiency ratios, partial work and leaks.
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