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Time & Work · Topic 2 of 6

⚡ Efficiency & Wages

3 exam question types, fully solved

Efficiency is just how much work someone does per day — their rate. The single most useful fact in this whole chapter is that time and efficiency are inverses: the faster worker takes less time, in exactly the flipped proportion.

Efficiency is the inverse of time

If A is twice as efficient as B, then A takes half the time. In general, efficiency ratio is the reverse of the time ratio:

If times are in ratio , efficiencies are in ratio (flip it).

• Time from efficiency: A is 25% more efficient than B. Efficiencies , so times . If B takes 25 days, A takes days.

• Men vs women: “3 men = 5 women” means their total efficiency is equal, so 1 man women. Convert everyone into one unit (say women), then it is an ordinary rate sum.

Work and wages: pay is shared in the ratio of work actually done, which equals the ratio of efficiencies (when all work the same number of days) — i.e. the reverse of the time ratio. If A alone takes 10 days and B 15 days for a job they did together, they split the money in the ratio .

🧱Time & Work LabTotal work = LCM units — no fractions
A is … as efficient as B
Together they finish in (days)
Total wage (₹)
Efficiency A : B =2 : 1→ flip →Time A : B =1 : 2
Total work = (2 + 1) × 12 = 36 units
Each day, A does2 units
Each day, B does1 units
Together per day2 + 1 = 3 units → 12 days ✓
A alone finishes in18 days
B alone finishes in36 days
Wage split — pay follows work done = efficiency ratio 2 : 1
A ₹600
B ₹300
A is 2× as efficient → efficiency A : B = 2 : 1, so the time ratio flips to 1 : 2. Give A 2 units/day and B 1 units/day → together 3 units/day × 12 days = 36 units of work. A alone: 36 ÷ 2 = 18 days · B alone: 36 ÷ 1 = 36 days. Wages ₹900 split 2 : 1 → ₹600 : ₹300.

A is twice as efficient as B, so if B needs 30 days, A needs days.

📝Practice Questions

Q1A is 3 times as efficient as B. Working together they finish a job in 6 days. A alone will take:

Q2A and B work together for 6 days and complete 2/3 of the work. A then finishes the rest alone, the whole job taking 9 days in all. A alone can do the full work in:

Q3A is three times as efficient as B. Together they complete a work in 9 days. A alone will take:

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Real exam questions — Efficiency & Wages

3 question types · 11 solved examples from real SSC papers

Efficiency is just the inverse of time — master “n times as efficient” and wage-sharing here, and a whole family of SSC Time & Work questions becomes instant.

How to solve this type
Fix the slower worker at 11 unit/day and scale the faster one (A is nn times as efficient ⇒\Rightarrow A =n=n units/day). Then use Work == Efficiency ×\times Time. Combined time =slower person’s timen+1=\dfrac{\text{slower person’s time}}{n+1}.

A is 3 times as efficient as B and finishes the job alone in 10 days. How many days will B alone take?

A25 daysB20 daysC15 daysD30 days

A is 4 times as efficient as B, and B alone finishes the work in 40 days. Working together, they finish in:

A6 daysB12 daysC10 daysD8 days

A is twice as efficient as B. Together they finish the work in 12 days. A alone will take:

A15 daysB20 daysC18 daysD24 days

A is twice as efficient as B. A works for 5 days and leaves; B then finishes the remaining work alone in 10 more days. A alone can do the whole work in:

A15 daysB8 daysC10 daysD12 days