Work Efficiency, Wages and Speed Strategy

The final piece ties the chapter together: efficiency ratios that let you compare workers instantly, wage sharing based on the work actually done, and the exam strategy that decides which of these questions to attempt in a speed test. These wrap-up ideas convert the formulas you have built into fast decisions, and the topic closes with the strategy that matters most in a sectional-timed prelims — knowing which sums to solve and which to leave alone.

Efficiency Ratios

Efficiency is inversely proportional to the time taken: the faster worker is the more efficient one. If A finishes in 10 days and B in 20, A is twice as efficient, so their efficiency ratio is 2:1 while their time ratio is 1:2 — always inverted. Phrases like 'A is 25 percent more efficient than B' translate to an efficiency ratio of 5:4, which flips to a time ratio of 4:5. Reading efficiency and time as inverse ratios lets you answer comparison questions without computing any actual days at all.

Efficiency ∝ 1 / time Efficiency ratio = inverse of the time ratio

Wage Sharing by Work Done

When workers are paid for a shared job, each person's wage is proportional to the work they personally complete, not to the days they show up. If A and B do a job in the work ratio 3:2, they split the total wage 3:2. The quickest route is to find each worker's per-day units, multiply by the days they actually worked, and share the money in that ratio. A more efficient worker earns a larger slice even in the same number of days, which is exactly what the ratio captures.

✗ Splitting wages equally because both worked the same days  |  ✓ Splitting wages in the ratio of units each one actually completed

Solved Examples

Example 1: A is twice as efficient as B, so their rates are 2 + 1 = 3 parts; if the job is 30 units, together they finish in 10 days. Example 2: A does 3 units/day, B does 2 units/day, and a 6-day job pays Rs 500; A's share = 18/30 × 500 = Rs 300, B's = Rs 200. Example 3: 'A is 50% more efficient than B' gives efficiency 3:2, so a time ratio of 2:3.

Speed Strategy for This Chapter

In the Numerical section you have roughly 34 seconds per question, so this chapter's word problems must be triaged. Direct formula sums — a single speed, a straightforward two-pipe fill, a plain combined-work question — should be attempted first because they finish in under a minute. Multi-stage problems, boats with several unknowns, or pipes opened at staggered times can devour three minutes, so mark them and return only if time remains. Deciding attempt-or-skip in the first ten seconds is worth more marks than raw calculation speed.

Putting the Chapter Together

Every topic in this chapter shares one engine: express each rate cleanly, combine rates by adding or subtracting, then divide the total by the combined rate. Speed-distance-time, relative speed, time-and-work and pipes are the same skill applied to distance, closing gaps, jobs and tanks in turn. Efficiency and wages simply attach ratios to that engine. Once you see the common structure you stop memorising four separate topics and instead carry one flexible method into the exam, which is exactly what a speed-based paper rewards.