Time & Work • Topic 4 of 4

Work & Wages

Pay is shared in the ratio of work actually done. If people work for the same time, that is just the ratio of their rates (efficiencies). Compute each person's share of the total work (rate x days worked), form the ratio, and split the wages accordingly. A partner who works fewer days earns proportionally less.

✅ Solved examples

1. A in 6 days, B in 12 days do a job together for 480. Shares?
Rates 1/6:1/12 = 2:1; A = 320, B = 160.
2. A, B, C in 10, 12, 15 days share 1500 for working together. C share?
LCM 60: rates 6:5:4; total 15 parts; C = 4/15 x 1500 = 400.
3. A works 4 days at rate 3 units/day, B works 6 days at 2 units/day; wage 700. A share?
Work 12 vs 12 = 1:1; A = 350.
4. A alone in 8, B in 12; they finish together and earn 1000. B share?
Rates 3:2 (LCM 24); B = 2/5 x 1000 = 400.

✏️ Practice — try these, take hints as needed

1. A in 5, B in 10, wage 600 (together). A share?
Rates 2:1.
2/3 x 600.
—
400
2. A in 6, B in 9, wage 750. B share?
Rates 3:2 (LCM 18).
2/5 x 750.
—
300
3. A,B,C in 4,6,8; wage 1300 (together). A share?
LCM 24: 6:4:3.
6/13 x 1300.
—
600
4. A in 10, B in 15, wage 500. A share?
Rates 3:2.
3/5 x 500.
—
300
5. A 5 days at 4/day, B 4 days at 5/day; wage 800. Shares?
Work 20 vs 20.
1:1.
—
400 each

📝 Topic test — 8 questions

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