Question 1

Two workers, R and S, have efficiencies in the ratio 3:2. If R can complete a job in 10 days, in how many days can S complete the same job?

Accepted Answer

Step 1: Efficiency ratio R:S = 3:2. Step 2: If R's efficiency is 3 units, S's efficiency is 2 units. Step 3: Since efficiency is inversely proportional to time, time ratio R:S = 2:3. Step 4: If R takes 10 days, S takes 10 × (3/2) = 15 days.

Question 2

H can do 1/5 of a work in 4 days. How many days will H take to complete the entire work?

Accepted Answer

Step 1: H completes 1/5 of work in 4 days. Step 2: To find time for full work, use: if 1/5 work takes 4 days, then full work (5/5) takes 4 × 5 = 20 days. Therefore, H takes 20 days to complete the entire work.

Question 3

A worker earns ₹500 per day. If he works for 12 days, what is his total wage?

Accepted Answer

Step 1: Identify daily wage = ₹500. Step 2: Number of days worked = 12. Step 3: Total wage = Daily wage × Number of days = 500 × 12 = ₹6000.

Question 4

A man is paid ₹40 per hour. If he works 8 hours a day for 5 days, what is his total earnings?

Accepted Answer

Step 1: Hourly wage = ₹40. Step 2: Hours per day = 8. Step 3: Number of days = 5. Step 4: Total hours worked = 8 × 5 = 40 hours. Step 5: Total earnings = 40 × 40 = ₹1600.

Question 5

Three workers can complete a task in 8 days. How many days will it take for 4 workers to complete the same task, assuming all workers work at the same rate?

Accepted Answer

Step 1: Total work = 3 workers × 8 days = 24 worker-days. Step 2: With 4 workers, days required = 24 worker-days ÷ 4 workers = 6 days.

Question 6

A contractor pays ₹600 per day to each worker. If 5 workers work for 10 days, what is the total amount paid by the contractor?

Accepted Answer

Step 1: Daily wage per worker = ₹600. Step 2: Number of workers = 5. Step 3: Number of days = 10. Step 4: Total amount = Daily wage × Number of workers × Number of days = 600 × 5 × 10 = ₹30,000.

Question 7

Worker X completes 1/4 of a job in 5 days. At this rate, in how many days will X complete the entire job?

Accepted Answer

Step 1: Worker X completes 1/4 of the job in 5 days. Step 2: To complete the full job (4/4), X needs 4 times as many days. Step 3: Total days = 5 × 4 = 20 days.

Question 8

Pipe A can fill a cistern in 12 hours, and Pipe B can empty it in 18 hours. If both pipes are opened together, how long will it take to fill the cistern?

Accepted Answer

Step 1: Rate of Pipe A = 1/12 per hour (filling). Step 2: Rate of Pipe B = 1/18 per hour (emptying). Step 3: Combined rate = 1/12 - 1/18 = (3 - 2)/36 = 1/36 per hour. Step 4: Time to fill = 1 ÷ (1/36) = 36 hours.

Question 9

Two workers, P and Q, are paid ₹600 per day and ₹400 per day respectively. They work together for 5 days and complete a job. If P works alone for 2 additional days to finish remaining work, what is the total amount paid for the job?

Accepted Answer

Step 1: Payment for P and Q working together for 5 days = (600 + 400) × 5 = 1000 × 5 = ₹5000. Step 2: Payment for P working alone for 2 days = 600 × 2 = ₹1200. Step 3: Total payment = 5000 + 1200 = ₹6200.

Question 10

The efficiency of X is 25% more than Y. If X can complete a task in 16 days, in how many days can Y complete the same task?

Accepted Answer

Step 1: Let Y's efficiency = e. Then X's efficiency = 1.25e. Step 2: X completes work in 16 days, so X's efficiency = 1/16 per day. Step 3: Therefore, 1.25e = 1/16, which gives e = 1/20 per day. Step 4: Y's efficiency = 1/20 per day means Y takes 20 days to complete the work.

Question 11

A contractor hires 15 workers to complete a road in 24 days. After 8 days, he hires 5 more workers. How many days in total will the project take to complete?

Accepted Answer

Step 1: Total work = 15 workers × 24 days = 360 worker-days. Step 2: Work completed in first 8 days = 15 × 8 = 120 worker-days. Step 3: Remaining work = 360 - 120 = 240 worker-days. Step 4: After hiring 5 more workers, total workers = 15 + 5 = 20. Step 5: Days needed for remaining work = 240 ÷ 20 = 12 days. Step 6: Total days = 8 + 12 = 20 days.

Question 12

A and B together can complete a job in 12 days. A alone can complete it in 20 days. If A works for 5 days and then B works alone for the remaining days, how much will B earn if the total wage for the job is ₹4,800?

Accepted Answer

Step 1: Find B's work rate. A's rate = 1/20 per day. Combined rate = 1/12 per day. So B's rate = 1/12 − 1/20 = (5−3)/60 = 2/60 = 1/30 per day. Step 2: Work done by A in 5 days = 5 × (1/20) = 1/4. Remaining work = 1 − 1/4 = 3/4. Step 3: Days B needs = (3/4) ÷ (1/30) = (3/4) × 30 = 22.5 days. Step 4: Wages are distributed by work done. A's share = (1/4) × 4800 = ₹1,200. B's share = (3/4) × 4800 = ₹3,600.

Question 13

Two workers P and Q are paid ₹500 per day each. P can complete a task in 24 days and Q can complete it in 36 days. They work together for some days, then P leaves and Q continues alone for 6 more days to finish the task. How much more does Q earn than P?

Accepted Answer

Step 1: Work rates: P = 1/24, Q = 1/36 per day. Combined rate = 1/24 + 1/36 = (3+2)/72 = 5/72 per day. Step 2: Let them work together for x days. Work done = x(5/72). Remaining work = 1 − 5x/72. Step 3: Q alone does remaining work in 6 days: 6(1/36) = 6/36 = 1/6. So 1 − 5x/72 = 1/6, which gives 5x/72 = 5/6, so x = 12 days. Step 4: P works 12 days, earns 12 × 500 = ₹6,000. Step 5: Q works 12 + 6 = 18 days, earns 18 × 500 = ₹9,000. Step 6: Difference = 9000 − 6000 = ₹3,000.

Question 14

Three workers X, Y, and Z can complete a project in 30, 40, and 60 days respectively. They work together for 5 days, then X leaves. Y and Z continue for 4 more days, then Z leaves and Y finishes alone. If the total payment is ₹12,000 and wages are distributed by work done, how much does Y receive?

Accepted Answer

Step 1: Work rates: X = 1/30, Y = 1/40, Z = 1/60 per day. Step 2: Work in first 5 days (all three) = 5(1/30 + 1/40 + 1/60) = 5(4+3+2)/120 = 5(9/120) = 45/120 = 3/8. Step 3: Remaining work = 5/8. Work by Y and Z in 4 days = 4(1/40 + 1/60) = 4(3+2)/120 = 20/120 = 1/6. Step 4: Work left for Y alone = 5/8 − 1/6 = (15−4)/24 = 11/24. Step 5: Y's total work = 5(1/40) + 4(1/40) + (11/24)(1/40) × 40 = 5/40 + 4/40 + 11/24 = 9/40 + 11/24 = (27+55)/120 = 82/120 = 41/60. Step 6: Y's wage = (41/60) × 12000 = ₹8,200.

Question 15

A contractor hires workers for a project. If 8 workers complete the work in 15 days, and the contractor pays ₹120 per worker per day, how much total wage must be paid? Later, the contractor decides to complete the same work in 10 days. If the daily wage per worker remains ₹120, how many workers are needed, and what is the additional wage cost compared to the original plan?

Accepted Answer

Step 1: Original plan: 8 workers × 15 days = 120 worker-days. Total wage = 120 × 120 = ₹14,400. Step 2: Work amount = 120 worker-days (constant). Step 3: New plan: 10 days, so workers needed = 120 ÷ 10 = 12 workers. Step 4: New total wage = 12 × 10 × 120 = ₹14,400. Step 5: Additional cost = 14,400 − 14,400 = ₹0.

Question 16

A and B work on a project with wages in the ratio 3:2. A can complete the work alone in 18 days and B can complete it alone in 27 days. They work together for 6 days, then A leaves and B continues alone. If B's total wage is ₹4,800, what is A's total wage?

Accepted Answer

Step 1: Work rates: A = 1/18, B = 1/27 per day. Step 2: Work in first 6 days (together) = 6(1/18 + 1/27) = 6(3+2)/54 = 6(5/54) = 30/54 = 5/9. Step 3: Remaining work = 4/9. Days for B alone = (4/9) ÷ (1/27) = (4/9) × 27 = 12 days. Step 4: A's total work = 6 × (1/18) = 6/18 = 1/3. B's total work = 6 × (1/27) + 12 × (1/27) = 18/27 = 2/3. Step 5: Work ratio A:B = (1/3):(2/3) = 1:2. Step 6: But wages are in ratio 3:2. This means wage per unit work: A gets 3k per unit, B gets 2k per unit. Step 7: A's wage = (1/3) × 3k = k. B's wage = (2/3) × 2k = 4k/3. So k:(4k/3) = 3:4. But we're told B earns ₹4,800. So 4k/3 = 4800, giving k = 3600. A's wage = 3600.

Question 17

Three workers M, N, and O are hired for a job. M's daily wage is ₹200, N's is ₹250, and O's is ₹300. M can complete the job in 30 days, N in 40 days, and O in 60 days. They work together for 8 days, then M and O leave and N continues alone for 10 more days. If the remaining work is completed by a fourth worker P in 5 days at ₹400 per day, what is the total wage paid for the entire project?

Accepted Answer

Step 1: Work rates: M = 1/30, N = 1/40, O = 1/60 per day. Step 2: Work in first 8 days (M, N, O together) = 8(1/30 + 1/40 + 1/60) = 8(4+3+2)/120 = 8(9/120) = 72/120 = 3/5. Step 3: Remaining work = 2/5. Step 4: N alone for 10 days = 10 × (1/40) = 10/40 = 1/4. Step 5: Work left for P = 2/5 − 1/4 = (8−5)/20 = 3/20. Step 6: P's rate = 1/5 per day (completes in 5 days). Check: 5 × (1/5) = 1 ✓. But P only does 3/20, which takes (3/20) ÷ (1/5) = (3/20) × 5 = 3/4 days. [Contradiction in problem statement: P works 5 days but only 3/4 days needed.] Assuming problem means P works until done (3/4 days): Step 7: M's wage = 8 × 200 = ₹1,600. N's wage = (8 + 10) × 250 = 18 × 250 = ₹4,500. O's wage = 8 × 300 = ₹2,400. P's wage = (3/4) × 400 = ₹300. Step 8: Total = 1600 + 4500 + 2400 + 300 = ₹8,800.

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