Time and Work DILR Sets for CAT: 3 Worked Examples

What happens when a Quant concept shows up wearing a DILR costume? Time and work is the textbook case. You know the formula cold from Quant prep, so you open the set, plug in rates, and answer the first question fast. Then the next three questions split the job across two teams, swap one worker mid-project, and ask how much is left after eight days. Suddenly the formula has nowhere to go, because the real difficulty was never the rate. It was the structure. Time and work DILR sets test whether you can map a tangle of constraints before you compute, and most strong Quant students skip that step entirely.

This guide fixes that. You will build an efficiency table, the single tool that turns these sets from messy to mechanical, and then watch it solve three full sets, one for each format CAT favours: project teams, production machines, and shift workers.

Why pure Quant fails on these sets

A Quant time and work question is a closed loop. It gives you the rates, asks one thing, and the answer falls out of a formula you have used a hundred times. There is no data to interpret because there is nothing hidden. Everything you need sits on the surface.

A DILR set inverts that. The rates are buried inside phrases like "Team B works twice as fast as Team C" or "Machine 2 needs 30 percent more time than Machine 1." Nothing is stated as a number until you extract it. Worse, the four questions rarely share a path. One asks for total days, the next asks who finished which order, the third introduces a breakdown on day five, and the fourth reverses the whole thing and asks for the cheapest allocation. If you solve question by question without a master layout, you redo the same extraction four times and run out of clock. This is exactly why the CAT exam rewards aspirants who read the full set before they touch a single question.

The fix is to treat the data as data. Read the full set first, pull every rate and constraint into one place, and only then start answering. This is the same discipline behind a clean DILR constraint notation system, where you commit the conditions to a fixed format before touching any question. For rate sets, that fixed format is the efficiency table.

The efficiency table method

The method has three moves, and they never change across set types.

1. Fix the total work. Pick a number for the whole job that divides cleanly by every completion time in the data. The LCM of those times is the safe default. Now the job is, say, 120 units instead of "1 project."
2. Convert each agent to a rate. If Team A finishes the 120-unit job alone in 20 days, Team A does 6 units a day. Write that as a row. Do this for every worker, machine, or team. The table now holds one efficiency value per agent.
3. Answer with arithmetic, not algebra. Combined output is a column sum. Work done by day eight is rate times eight. Work remaining is a subtraction. The four questions stop being equations and become lookups on your table.

The reason this beats raw formulas in DILR is that it scales. Two agents or six, one time window or three, the table absorbs all of it without new setup. You build it once and harvest four answers. Below, the same three moves run three different sets.

Worked set 1: project teams of different efficiency

Notice that not one question needed a fresh equation. Every answer came from the three-row table by adding rates and subtracting units. That is the payoff for mapping first. This same set-up scales straight into profit and loss DILR sets, where cost per unit replaces work per day but the table logic is identical.

Worked set 2: machines with different production rates

The trap in machine sets is the parallel clock. Two orders run at once, so you cannot add their times. You track each order on its own timeline and read the total off whichever finishes last. The table holds the rates steady while the timelines move independently.

Worked set 3: workers covering three shifts

Shift sets add a second layer: the order of shifts matters for the last day. The table gives you per-shift output, but you still have to walk the final partial day shift by shift. Before you commit to a set like this in the exam, it helps to rate the set's difficulty in 60 seconds so you know whether the partial-day logic is worth your time or a trap to skip.

Common questions on time and work DILR sets

Build the efficiency table on every rate set you attempt and the structure becomes muscle memory before the exam. Once you can see project teams, machines, and shift workers as three faces of the same table, this whole family of sets stops costing you setup time. When you want to drill them in sequence, the full library of CAT preparation guides covers every DILR set type, and you can check how a stronger DILR section moves your overall score with the CAT score predictor before you sit your next mock.