Question 1

The work efficiency of A is 3 times that of B. If A and B together complete a project in 9 days, how many days will B alone take to complete the project?

Accepted Answer

Step 1: Let B's efficiency = x work per day. Then A's efficiency = 3x work per day. Step 2: Combined efficiency = 3x + x = 4x work per day. Step 3: Since they complete work in 9 days: 4x × 9 = 1 (total work), so 4x = 1/9, thus x = 1/36. Step 4: B's efficiency = 1/36 work per day. Step 5: Time for B alone = 1 ÷ (1/36) = 36 days. Therefore, answer is 36 days.

Question 2

A worker can complete a job in 12 days. If he is paid ₹480 for the entire job, what is his daily wage?

Accepted Answer

Step 1: Total payment = ₹480. Step 2: Number of days = 12. Step 3: Daily wage = Total payment ÷ Number of days = 480 ÷ 12 = ₹40 per day.

Question 3

A worker earns ₹600 for 8 days of work. How much will he earn for 20 days of work at the same rate?

Accepted Answer

Step 1: Daily wage = 600 ÷ 8 = ₹75 per day. Step 2: Wage for 20 days = 75 × 20 = ₹1500.

Question 4

A and B together earn ₹2400 in 6 days. If A earns ₹200 per day and B earns ₹150 per day, how much does A earn in 10 days?

Accepted Answer

Step 1: A's daily wage = ₹200. Step 2: A's earnings in 10 days = 200 × 10 = ₹2000. (Note: The combined earnings information is extra context but not needed for this calculation.)

Question 5

A job requires 120 worker-days to complete. If 5 workers are assigned to the job, how many days will it take to finish?

Accepted Answer

Step 1: Total work = 120 worker-days. Step 2: Number of workers = 5. Step 3: Time required = Total work ÷ Number of workers = 120 ÷ 5 = 24 days.

Question 6

D completes 1/5 of a work in 4 days. At this rate, how many days will D take to complete the entire work?

Accepted Answer

Step 1: D completes 1/5 work in 4 days. Step 2: To complete 5/5 (entire work), D needs 5 × 4 = 20 days. Therefore, D takes 20 days to complete the entire work.

Question 7

Three workers P, Q, and R are paid in the ratio 3:4:5 for a job. If the total payment is ₹14,400 and they work for 8, 10, and 12 days respectively, what is Q's daily wage?

Accepted Answer

Step 1: Total payment is distributed in ratio 3:4:5. Sum of ratio parts = 3+4+5 = 12. Step 2: Q's share = (4/12) × 14,400 = ₹4,800. Step 3: Q works for 10 days. Step 4: Q's daily wage = 4,800 ÷ 10 = ₹480.

Question 8

A worker is paid ₹500 per day. If he works for 18 days and completes 3/4 of a project, what is his total wage for completing the entire project at the same daily rate?

Accepted Answer

Step 1: Worker completes 3/4 of project in 18 days. Step 2: To complete entire project (4/4), days needed = 18 ÷ (3/4) = 18 × (4/3) = 24 days. Step 3: Total wage = 24 × ₹500 = ₹12,000. Therefore, total wage for the entire project is ₹12,000.

Question 9

A contractor hires workers at ₹400 per day. If 5 workers complete a project in 16 days, how much total wage must be paid if the same project is to be completed in 10 days using workers at the same daily rate?

Accepted Answer

Step 1: Total work = 5 workers × 16 days = 80 worker-days. Step 2: To complete in 10 days: workers needed = 80 ÷ 10 = 8 workers. Step 3: Total wage = 8 workers × 10 days × ₹400/day = ₹32,000. Therefore, total wage is ₹32,000.

Question 10

A and B are paid in the ratio 3:2 for a project. If A receives ₹9,000 for completing 3/5 of the work, what is B's wage for completing the remaining work at the same rate per unit of work?

Accepted Answer

Step 1: A completes 3/5 of work and receives ₹9,000. Step 2: Rate per unit work = ₹9,000 ÷ (3/5) = ₹9,000 × (5/3) = ₹15,000 per full project. Step 3: B completes remaining 2/5 of work. Step 4: B's wage = (2/5) × ₹15,000 = ₹6,000. Therefore, B's wage is ₹6,000.

Question 11

A's efficiency is twice that of B. If A and B together can complete a project in 9 days, how many days will B alone take to complete it?

Accepted Answer

Step 1: Let B's rate = 1/x per day. Then A's rate = 2/x per day (twice efficient). Step 2: Combined rate = 1/x + 2/x = 3/x per day. Step 3: They complete in 9 days, so 3/x = 1/9. Step 4: Solving: 3 × 9 = x, so x = 27 days.

Question 12

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: Net rate = 1/12 - 1/18 = (3-2)/36 = 1/36 per hour. Step 4: Time to fill = 1 ÷ (1/36) = 36 hours.

Question 13

A can complete a project 40% faster than B. If both work together, they can finish the project in 12 days. In how many days can A alone complete the project?

Accepted Answer

Step 1: Let B's time = b days. A is 50% faster, so A takes 2/3 of B's time: a = 2b/3 days. Step 2: A's rate = 3/(2b) per day. B's rate = 1/b per day. Step 3: Combined rate = 3/(2b) + 1/b = 3/(2b) + 2/(2b) = 5/(2b) per day. Step 4: Combined time = 12 days, so 5/(2b) = 1/12. Step 5: 2b = 60 → b = 30 days. Step 6: A's time = 2 × 30/3 = 20 days.

Question 14

A contractor hires workers to complete a bridge in 20 days. After 5 days, he realizes the work is only 15% complete. He then increases the workforce by 60%. How many additional days beyond the original 20 days will be needed to finish the project?

Accepted Answer

Step 1: After 5 days, 15% complete → original rate = 15/5 = 3% per day. Step 2: Remaining work = 85%. Step 3: New workforce = 1.6 × original → new rate = 1.6 × 3% = 4.8% per day. Step 4: Days for remaining 85% = 85 ÷ 4.8 = 17.708 days ≈ 17.71 days. Step 5: Total time = 5 + 17.71 = 22.71 ≈ 23 days. Step 6: Additional days = 23 - 20 = 3 days.

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