Time & Work • Topic 1 of 4

Work & Efficiency

If A does a job in 'a' days, A's rate is 1/a of the job per day. Efficiency is just rate: someone twice as efficient finishes in half the time. The LCM method removes fractions — set total work = LCM of the days, convert each person's days to units/day, then reason with whole numbers. Men-days (or man-hours) is conserved: M1 x D1 = M2 x D2 for the same job.

✅ Solved examples

1. A does a job in 12 days, B in 6 days. Who is more efficient and by how much?
Rates 1/12 and 1/6; B is twice as efficient as A (B does 2 units to A 1).
2. A finishes in 10 days. How much work in 4 days?
4 x (1/10) = 2/5 of the work.
3. 15 men build a wall in 8 days. How many men for the same wall in 6 days?
Men-days constant: 15x8 = 120 = M x 6 -> M = 20.
4. A is 25% more efficient than B. If B takes 20 days, A takes?
A rate = 1.25 of B; time = 20/1.25 = 16 days.

✏️ Practice — try these, take hints as needed

1. A in 9 days. Work in 3 days?
3 x 1/9.
—
—
1/3
2. 12 men, 10 days. Men for 8 days?
12x10 = 120.
120/8.
—
15
3. A twice as efficient as B; B takes 18 days. A?
Half the time.
18/2.
—
9 days
4. A in 16 days; A is 60% more efficient than B. B?
B rate = A/1.6.
B time = 16 x 1.6.
—
25.6 days
5. 20 women, 12 days. Days for 15 women?
20x12 = 240.
240/15.
—
16 days

📝 Topic test — 8 questions

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