Work and Wages Competitive Exams
50 questions · Mathematics
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Question 1 of 50
A and B can do a job in 10 and 15 days respectively. With C's help all three finish it in 5 days, for a total payment of Rs 7,500. C's share is
ExplanationC's rate = 1/5 − 1/10 − 1/15 = 1/30. Ratio A : B : C = 3 : 2 : 1, so C gets 7,500/6 = Rs 1,250.
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Question 2 of 50
A and B together can do a job in 6 days, B and C in 8 days, and C and A in 12 days. A alone can do it in
Explanation2(A + B + C) = 1/6 + 1/8 + 1/12 = 3/8, so A + B + C = 3/16. A = 3/16 − 1/8 = 1/16 per day.
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Question 3 of 50
A completes a job in 5 days and B in 8 days. The ratio of efficiencies of A : B is
ExplanationEfficiency is inversely proportional to time, so ratio = 1/5 : 1/8 = 8 : 5.
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Question 4 of 50
A can do a work in 20 days. After working for 5 days, the fraction of work still left is
ExplanationWork done = 5/20 = 1/4, so 1 − 1/4 = 3/4 remains.
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Question 5 of 50
A can complete a piece of work in 10 days. The part of the work A does in 1 day is
ExplanationIf a job takes n days, one day's work is 1/n.
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Question 6 of 50
A is four times as efficient as B. Together they complete a job in 10 days. B alone would take
ExplanationLet B's rate = x; then 5x = 1/10, so x = 1/50.
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Question 7 of 50
A worker earns Rs 80 per hour for the first 8 hours of a day and 1.5 times that rate for overtime. He works 10 hours a day for 5 days. His total earnings are
ExplanationPer day: 8 × 80 = 640 plus 2 × 120 = 240, total 880. Over 5 days: Rs 4,400.
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Question 8 of 50
A is twice as fast as B. Working together they finish a job in 12 days. A alone would take
ExplanationLet B's rate = x, A's = 2x. 3x = 1/12, so x = 1/36 and A's rate = 1/18; 18 days.
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Question 9 of 50
A can do a job in 16 days and B in 24 days. They start together, but A leaves 4 days before the job is completed. The total time taken is
ExplanationLet total be T days. B works T days and A works T − 4 days: (T − 4)/16 + T/24 = 1 → 3(T − 4) + 2T = 48 → T = 12.
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Question 10 of 50
A works for 3 days and B works for 2 days at the same daily wage. They share Rs 1,200 for the job. A's share is
ExplanationRatio of wages = 3 : 2, so A gets 3/5 × 1,200 = Rs 720.
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Question 11 of 50
A and B together can do a job in 10 days. A alone can do it in 15 days. If the job earns Rs 6,000 in total, B's share is
ExplanationB's rate = 1/10 − 1/15 = 1/30. Ratio A : B = 2 : 1, so B gets 1/3 × 6,000 = Rs 2,000.
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Question 12 of 50
A job can be done by 6 men in 15 days. If one man does the work of two women, then 10 men and 10 women will do it in
ExplanationWork = 90 man-days. 10 men + 10 women = 10 + 5 = 15 man-equivalents; 90 ÷ 15 = 6 days.
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Question 13 of 50
A, B and C can do a job alone in 10, 15 and 30 days respectively. Working together they finish it in
Explanation1/10 + 1/15 + 1/30 = 3/30 + 2/30 + 1/30 = 6/30 = 1/5, so 5 days.
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Question 14 of 50
8 workers together earn Rs 32,000 in 10 days at an equal rate. The daily wage of each worker is
ExplanationTotal worker-days = 8 × 10 = 80; 32,000 ÷ 80 = Rs 400.
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Question 15 of 50
A, B and C work for 10, 12 and 15 days at daily wages of Rs 200, Rs 150 and Rs 100 respectively. The total wages paid are
Explanation2,000 + 1,800 + 1,500 = Rs 5,300.
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Question 16 of 50
A and B together can finish a job in 12 days, B and C in 15 days, and C and A in 20 days. Working all together they will finish it in
ExplanationAdding: 2(A + B + C) = 1/12 + 1/15 + 1/20 = 1/5, so A + B + C = 1/10 per day.
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Question 17 of 50
A labourer earns Rs 600 per day. His total earnings for 25 days of work are
ExplanationTotal wage = daily wage × days = 600 × 25.
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Question 18 of 50
30 workers can complete a road in 40 days. After 10 days, 20 more workers join. The remaining work is finished in
ExplanationTotal = 1,200 man-days; done 300; remaining 900 ÷ 50 workers = 18 days.
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Question 19 of 50
A and B together can do a job in 12 days. A alone can do it in 20 days. If they are paid Rs 3,000 in total, A's share is
ExplanationB's rate = 1/12 − 1/20 = 1/30. Ratio A : B = 3 : 2, so A gets 3/5 × 3,000 = Rs 1,800.
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Question 20 of 50
A can do a job in 20 days and B in 30 days. A starts alone and works for 5 days; then B joins and they finish together. The total payment is Rs 5,000, shared in proportion to work done. B's share is
ExplanationA's 5 days = 1/4 done. Remaining 3/4 at 1/12 per day = 9 days. B works 9 days → 9/30 = 3/10 of job, so B gets 3/10 × 5,000 = Rs 1,500.
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Question 21 of 50
A can do a job in 12 days and B can do it in 6 days. Working together, they finish it in
ExplanationCombined rate = 1/12 + 1/6 = 3/12 = 1/4 per day, so 4 days.
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Question 22 of 50
A worker has an efficiency of 4 units of work per day. The number of days to complete 120 units is
ExplanationDays = total work ÷ efficiency = 120 ÷ 4 = 30.
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Question 23 of 50
A can do a job in 10 days and B in 15 days. They work on alternate days, A starting first. The job is completed in
ExplanationTwo days of work = 1/10 + 1/15 = 1/6. Six such pairs (12 days) complete exactly 1 job.
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Question 24 of 50
A works for 5 days with efficiency 3 and B works for 6 days with efficiency 2. Wages of Rs 4,500 are shared in proportion to work done. A's share is
ExplanationWork done: A = 5 × 3 = 15, B = 6 × 2 = 12; ratio 5 : 4. A's share = 5/9 × 4,500 = Rs 2,500.
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Question 25 of 50
A man can paint a wall in 6 hours and a woman can do it in 9 hours. Working together they will take
Explanation1/6 + 1/9 = 5/18 per hour, so 18/5 = 3.6 hours.
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Question 26 of 50
A worker is paid Rs 15 per item. He makes 18 items a day for 20 days. His total earnings are
ExplanationItems = 18 × 20 = 360; earnings = 360 × 15 = Rs 5,400.
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Question 27 of 50
A works twice as fast as B. If B alone can complete a job in 24 days, A alone can complete it in
ExplanationDouble the speed means half the time.
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Question 28 of 50
A can do a work in 20 days. B is 25% more efficient than A. B alone will complete the work in
ExplanationTime is inversely proportional to efficiency: 20 ÷ 1.25 = 16 days.
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Question 29 of 50
A, B and C work for 3, 4 and 5 days respectively at equal daily wages. The total wages are Rs 4,800. B's share is
ExplanationRatio = 3 : 4 : 5, total 12 parts. Each part = Rs 400, so B gets 4 × 400 = Rs 1,600.
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Question 30 of 50
A can do a job in 8 days and B in 12 days. They start together, but A leaves after 2 days, and B finishes the rest. The total time taken is
ExplanationIn 2 days, together they do 2 × 5/24 = 5/12. Remaining 7/12 takes B 7/12 × 12 = 7 days, so total = 2 + 7 = 9 days.
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Question 31 of 50
A can do a work in 15 days and B in 10 days. Working together they will finish it in
Explanation1/15 + 1/10 = 5/30 = 1/6 per day, so 6 days.
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Question 32 of 50
The efficiencies of A and B are in the ratio 3 : 2. Together they complete a job in 12 days. B alone would take
ExplanationTotal work = 12 × 5 = 60 units; B does 2 units per day, so 60 ÷ 2 = 30 days.
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Question 33 of 50
A is 50% more efficient than B. If B can finish a work in 30 days, A alone will take
ExplanationEfficiency ratio A : B = 3 : 2, so time ratio = 2 : 3; A = 30 × 2/3 = 20 days.
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Question 34 of 50
A can complete a job in 12 days and B in 18 days. Together they will finish it in
ExplanationTake work = 36 units: A = 3/day and B = 2/day; 36 ÷ 5 = 7.2 days.
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Question 35 of 50
A, B and C can do a job alone in 30, 45 and 90 days respectively. The ratio of their efficiencies is
ExplanationTaking the total work as LCM = 90 units: A = 3, B = 2, C = 1 unit per day.
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Question 36 of 50
A did 3/7 of a job and B did the remaining part. If the total payment is Rs 7,000 and wages are in proportion to work done, B's share is
ExplanationB did 4/7 of the job, so B gets 4/7 × 7,000 = Rs 4,000.
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Question 37 of 50
A is 20% less efficient than B. If A can complete a job in 25 days, B alone will take
ExplanationA's efficiency = 0.8 × B's, so B's time = 25 × 0.8 = 20 days.
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Question 38 of 50
If the efficiency of a worker increases by 25%, the time taken to complete the same job
ExplanationNew time = 1/1.25 = 0.8 of the old time, a 20% decrease.
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Question 39 of 50
A, B and C can do a job alone in 10, 15 and 30 days. They finish it together and share Rs 1,800. C's share is
ExplanationRatio of rates = 3 : 2 : 1, so C gets 1/6 × 1,800 = Rs 300.
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Question 40 of 50
A and B together can finish a job in 8 days. A alone can finish it in 12 days. B alone can finish it in
ExplanationB's rate = 1/8 − 1/12 = 1/24 per day.
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Question 41 of 50
12 men can complete a job in 18 days. After 6 days, 6 more men join. The remaining work is finished in
ExplanationTotal work = 216 man-days; done = 72; remaining 144 man-days ÷ 18 men = 8 days.
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Question 42 of 50
Contractor X employs 4 men for 5 days and Contractor Y employs 6 men for 5 days. A total of Rs 5,000 is divided in proportion to man-days. X receives
ExplanationMan-days: X = 20, Y = 30, ratio 2 : 3. X's share = 2/5 × 5,000 = Rs 2,000.
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Question 43 of 50
A can do a job in 12 days and B in 24 days. Working together they operate at only 80% of their combined efficiency. They will complete the job in
ExplanationCombined rate = 1/12 + 1/24 = 1/8. At 80%: 1/10 per day, so 10 days.
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Question 44 of 50
20 men can build a wall in 30 days. After 10 days, 10 men leave. The remaining work will be finished in a further
ExplanationTotal = 600 man-days; done 200; remaining 400 ÷ 10 men = 40 days.
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Question 45 of 50
A can do a job in 6 days and B in 12 days. They finish it together and receive Rs 900. A's share is
ExplanationIn the same time, work done is in the ratio of rates 1/6 : 1/12 = 2 : 1, so A gets 2/3 × 900 = Rs 600.
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Question 46 of 50
A is twice as efficient as B, and B is twice as efficient as C. Together the three finish a job in 8 days. A alone would take
ExplanationEfficiencies are 4 : 2 : 1, total 7 units/day. Work = 8 × 7 = 56 units; A takes 56 ÷ 4 = 14 days.
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Question 47 of 50
A works 6 hours a day for 10 days and B works 8 hours a day for 9 days at the same hourly wage. Total wages are Rs 5,280. A's share is
ExplanationHours: A = 60, B = 72, ratio 5 : 6. A's share = 5/11 × 5,280 = Rs 2,400.
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Question 48 of 50
6 men can complete a piece of work in 10 days. 15 men (of the same efficiency) will complete it in
ExplanationTotal work = 6 × 10 = 60 man-days; 60 ÷ 15 = 4 days.
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Question 49 of 50
A can do a job in 9 days and B in 18 days. A works alone for 3 days and then leaves. B completes the rest in
ExplanationA does 3/9 = 1/3 of the job. Remaining 2/3 ÷ (1/18) = 12 days.
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Question 50 of 50
A and B together can complete a job in 12 days. They work together for 4 days, then A leaves and B finishes the rest in 16 more days. B alone can complete the job in
ExplanationAfter 4 days, 1/3 is done, so 2/3 remains. B does 2/3 in 16 days, so the whole job takes 16 × 3/2 = 24 days.
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