Quantitative Aptitude

Work and Wages: Practice Questions with Answers

14 practice questions on Work and Wages, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   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.

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   Answer: 40/3 days ≈ 13.3 days

   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.

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2. Q.2

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

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   Answer: ₹1200

   Solution:

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

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3. Q.3

   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.

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   Answer: ₹960

   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.

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4. Q.4

   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.

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   Answer: A = ₹800, B = ₹1,200

   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.

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5. Q.5

   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.

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   Answer: ₹300

   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.

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6. Q.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.

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   Answer: A = ₹800, B = ₹4,000

   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.

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7. Q.7

   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.

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   Answer: ₹1800

   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.

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8. Q.8

   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.

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   Answer: ₹400

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9. Q.9

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

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   Answer: ₹800

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10. Q.10

    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.

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    Answer: ₹1200

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11. Q.11

    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.

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

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12. Q.12

    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.

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

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13. Q.13

    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.

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    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.

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14. Q.14

    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.

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    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.

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