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Work and Wages Solved Questions

When people work together and get paid as a group, the total wage is split in the same ratio as how much work each person actually did — which, for the same time worked, is the ratio of their individual work rates (1/days taken). This page covers that rule, what changes when people work UNEQUAL numbers of days, and reverse problems, with several fully worked examples.

Written by Mahesh Srivastava, Founder of Pariksha Saathi. Published: 2026-10-05. Editorial standards & corrections

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The concept, quickly

  • If everyone works for the SAME number of days, wages are split in the ratio of their individual one-day work rates (1/days each person alone would take) — faster workers get a bigger share.
  • Find each person’s one-day work rate first (1/days alone), simplify the ratio between them, and only then divide the total wage in that ratio.
  • For three or more people, the rate of the one not given directly can be found by subtracting the known rates from the combined rate — exactly like Time and Work.
  • A larger wage share does not always mean more DAYS worked — it means a HIGHER work rate (faster individual completion time), since everyone here works the same number of days together.
  • The "split by rate ratio" rule above only applies when everyone works the SAME number of days. If someone works fewer days than another (joins late, leaves early, or the days worked are simply stated as different), wages must be split by actual WORK DONE — each person's rate × the number of days THEY actually worked — not by the raw one-day rates alone.
  • To handle this, compute each person's actual fraction of the job completed (rate × their own days worked), confirm these fractions add up to the whole job (1), and use those fractions — not the bare rates — as the wage-split ratio.

Worked examples

1. A can complete a work in 10 days and B can complete the same work in 15 days. They work together and complete it, earning a total of ₹3000. Find A’s share.

Solution

  1. A’s one-day rate = 1/10, B’s = 1/15. Ratio A : B = 1/10 : 1/15 = 15 : 10 = 3 : 2 (multiplying both by 30).
  2. A’s share = 3/5 × ₹3000 = ₹1800.

Answer: ₹1800

2. Using the same data (A in 10 days, B in 15 days, total wage ₹3000), find B’s share.

Solution

  1. From the same 3 : 2 ratio, B’s share = 2/5 × ₹3000 = ₹1200.

Answer: ₹1200

3. A, B and C together can complete a work in 6 days. A alone can do it in 12 days, and B alone in 18 days. Working together, they earn ₹1800. Find C’s share.

Solution

  1. Combined rate = 1/6. A’s rate = 1/12, B’s rate = 1/18.
  2. C’s rate = 1/6 − 1/12 − 1/18. Using a common denominator of 36: 6/36 − 3/36 − 2/36 = 1/36.
  3. Ratio A : B : C = 3/36 : 2/36 : 1/36 = 3 : 2 : 1, total 6 parts. C’s share = 1/6 × ₹1800 = ₹300.

Answer: ₹300

4. A and B together can complete a work in 12 days. A alone can do it in 20 days. Working together, they earn ₹2400. Find B’s share.

Solution

  1. Combined rate = 1/12, A’s rate = 1/20. B’s rate = 1/12 − 1/20. Using a common denominator of 60: 5/60 − 3/60 = 2/60.
  2. Ratio A : B = 3/60 : 2/60 = 3 : 2, total 5 parts. B’s share = 2/5 × ₹2400 = ₹960.

Answer: ₹960

5. A can complete a work in 10 days and B in 15 days. A works on the job for 4 days and B works for 9 days (not necessarily at the same time), and together they just complete the work. If the total wage is ₹2000, find each person's share based on actual work done.

Solution

  1. A's actual work = 4 × (1/10) = 2/5. B's actual work = 9 × (1/15) = 3/5. Check: 2/5 + 3/5 = 1, the whole job — consistent.
  2. Since the days worked are unequal, split by actual work done, not by the bare rates: ratio = 2/5 : 3/5 = 2 : 3.
  3. A's share = (2/5) × 2,000 = ₹800. B's share = (3/5) × 2,000 = ₹1,200.

Answer: A = ₹800, B = ₹1,200

6. A and B together can complete a work in 12 days. They work together for 4 days, after which A leaves and B completes the remaining work alone in 16 more days. If the total wage for the whole job is ₹4,800, find each person's share based on actual work done.

Solution

  1. Combined rate = 1/12. Work done in the first 4 days = 4/12 = 1/3, so the remaining work = 2/3.
  2. B alone finishes 2/3 in 16 days, so B's rate = (2/3)/16 = 1/24. Then A's rate = 1/12 − 1/24 = 1/24 (the same as B's, in this case).
  3. During the first 4 days, A contributed 4 × 1/24 = 1/6, and B also contributed 4 × 1/24 = 1/6. B then contributed a further 2/3 alone. B's total = 1/6 + 2/3 = 5/6. A's total = 1/6. (Check: 1/6 + 5/6 = 1.)
  4. Wage ratio A : B = 1/6 : 5/6 = 1 : 5. A's share = (1/6) × 4,800 = ₹800. B's share = (5/6) × 4,800 = ₹4,000.

Answer: A = ₹800, B = ₹4,000

7. A and B, working together for the same number of days, earn a total wage split in the ratio 3 : 2. If B can complete the work alone in 20 days, find how many days A would take alone.

Solution

  1. Since the wage ratio (with equal days worked) equals the rate ratio: rate A : rate B = 3 : 2.
  2. rate B = 1/20, so rate A = (3/2) × (1/20) = 3/40.
  3. A's time alone = 1 / (3/40) = 40/3 ≈ 13.3 days.

Answer: 40/3 days ≈ 13.3 days

Try these yourself

Find the work-rate ratio first (or the actual-work ratio, if the days worked differ), then split the wage.

1. A can complete a work in 8 days and B can complete it in 12 days. They work together and earn ₹2000 total. Find A’s share.

Answer: ₹1200

2. Using the same data (A in 8 days, B in 12 days, total wage ₹2000), find B’s share.

Answer: ₹800

3. A, B and C together can complete a work in 4 days. A alone takes 10 days and B alone takes 15 days. If they earn ₹1200 together, find C’s share.

Answer: ₹400

4. A can complete a work in 12 days and B in 8 days. A works for 3 days and B works for 6 days, completing the work exactly. If the total wage is ₹1,400, find each person's share.

Answer: A = ₹350, B = ₹1,050. A's work = 3/12 = 1/4; B's work = 6/8 = 3/4; ratio 1:3.

5. A and B together can complete a work in 15 days. They work together for 5 days, after which A leaves and B completes the remaining work alone in 20 more days. If the total wage is ₹3,000, find each person's share.

Answer: A = ₹500, B = ₹2,500. Combined rate 1/15; both end up with equal individual rates of 1/30; A's total work = 1/6, B's = 5/6.

6. A and B, working together for the same number of days, earn a wage split in the ratio 2 : 3. If A can complete the work alone in 15 days, find how many days B would take alone.

Answer: 10 days. rate A = 1/15; rate B = (3/2) × (1/15) = 1/10.

7. A, B and C together can complete a work in 8 days. A alone takes 20 days and B alone takes 24 days. If they earn ₹1,440 together, find C's share.

Answer: ₹384. C's rate = 1/8−1/20−1/24 = 1/30; ratio A:B:C = 6:5:4; C's share = (4/15)×1,440.

All 14 practice questions on Work and Wages, with answers →

Where this comes up

Work and Wages is tested directly in the Quantitative/Numerical Aptitude section of exams Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — as a standard extension of Time and Work questions.

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