Question 1

A and B together can complete a piece of work in 12 days. If A's daily wage is ₹500 and B's daily wage is ₹700, and they are paid in the ratio of work done, how much will B receive if the total payment for the completed work is ₹14,400?

Accepted Answer

Step 1: A and B together complete work in 12 days, so combined work rate = 1/12 per day. Step 2: A's daily wage is ₹500 and B's daily wage is ₹700. The ratio of their daily wages = 500:700 = 5:7. Step 3: Since payment is in the ratio of work done, and work done is proportional to daily wage (assuming same number of days worked), B's share = (7/(5+7)) × 14,400 = (7/12) × 14,400 = ₹8,400.

Question 2

A, B, and C working together can complete a project in 12 days. A and B together can complete it in 18 days. If A is paid ₹500 per day, B is paid ₹400 per day, and C is paid ₹300 per day, then what is C's share of the total wages if the project is completed in 12 days and wages are distributed in the ratio of work done?

Accepted Answer

Step 1: Find C's work rate. A+B+C complete in 12 days, so combined rate = 1/12 per day. A+B complete in 18 days, so combined rate = 1/18 per day. Therefore, C's rate = 1/12 − 1/18 = (3−2)/36 = 1/36 per day. Step 2: Find individual rates. Let A's rate = a, B's rate = b. We know a + b = 1/18 and daily wages are A:B:C = 500:400:300 = 5:4:3. Since wages are proportional to daily rates (work rate × daily wage = contribution), we have 5a = 4b (from wage ratio). Solving: a = 4k, b = 5k for some k. Then 4k + 5k = 1/18, so k = 1/162. Thus a = 4/162 = 2/81, b = 5/162. Step 3: Verify C's rate = 1/36 = 4.5/162 (consistent). Step 4: Work done by each in 12 days: A does 12 × (2/81) = 24/81 = 8/27. B does 12 × (5/162) = 60/162 = 10/27. C does 12 × (1/36) = 12/36 = 1/3 = 9/27. Total = (8+10+9)/27 = 27/27 ✓. Step 5: Total wages = (500 + 400 + 300) × 12 = 1200 × 12 = ₹14,400. Step 6: C's share = (9/27) × 14,400 = (1/3) × 14,400 = ₹4,800.

Question 3

A worker earns ₹15 per hour. If he works 8 hours a day for 6 days, what is his total earnings?

Accepted Answer

Step 1: Hourly wage = ₹15. Step 2: Hours per day = 8. Step 3: Number of days = 6. Step 4: Total hours worked = 8 × 6 = 48 hours. Step 5: Total earnings = 15 × 48 = ₹720.

Question 4

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

Accepted Answer

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

Question 5

A man is paid ₹250 per day for regular work and ₹400 per day for overtime work. If he works 5 regular days and 3 overtime days in a week, what is his total weekly wage?

Accepted Answer

Step 1: Regular wage = ₹250 per day. Step 2: Regular days worked = 5. Step 3: Regular earnings = 250 × 5 = ₹1250. Step 4: Overtime wage = ₹400 per day. Step 5: Overtime days = 3. Step 6: Overtime earnings = 400 × 3 = ₹1200. Step 7: Total weekly wage = 1250 + 1200 = ₹2450.

Question 6

If 5 workers can complete a project in 20 days, how many days will 8 workers take to complete the same project, assuming all workers work at the same rate?

Accepted Answer

Step 1: Total work = 5 workers × 20 days = 100 worker-days. Step 2: With 8 workers, number of days = Total work ÷ Number of workers = 100 ÷ 8 = 12.5 days.

Question 7

A contractor employs 20 workers to complete a project in 24 days. If he wants to complete the same project in 16 days, how many additional workers does he need to hire (assuming all workers work at the same rate)?

Accepted Answer

Step 1: Total work = 20 workers × 24 days = 480 worker-days. Step 2: For 16 days, required workers = 480 ÷ 16 = 30 workers. Step 3: Additional workers needed = 30 - 20 = 10 workers.

Question 8

A man earns ₹15 per hour. If he works 8 hours a day for 6 days, what is his total earnings?

Accepted Answer

Step 1: Hourly wage = ₹15. Step 2: Hours per day = 8. Step 3: Number of days = 6. Step 4: Total hours worked = 8 × 6 = 48 hours. Step 5: Total earnings = 15 × 48 = ₹720.

Question 9

Two workers A and B together complete a job in 8 days. If A alone can complete the same job in 12 days, in how many days can B alone complete it?

Accepted Answer

Step 1: A's work rate = 1/12 per day. Step 2: Combined work rate of A and B = 1/8 per day. Step 3: B's work rate = 1/8 − 1/12 = (3−2)/24 = 1/24 per day. Step 4: B alone completes the job in 24 days.

Question 10

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

Accepted Answer

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

Question 11

A worker is paid ₹480 for 6 days of work. At the same rate, how much will he earn for 9 days of work?

Accepted Answer

Step 1: Daily wage = ₹480 ÷ 6 = ₹80 per day. Step 2: Wage for 9 days = ₹80 × 9 = ₹720.

Question 12

A contractor hires 8 workers to complete a job in 15 days. After 5 days, he hires 4 additional workers. In how many more days will the job be completed?

Accepted Answer

Step 1: Total work = 8 × 15 = 120 worker-days. Step 2: Work completed in 5 days = 8 × 5 = 40 worker-days. Step 3: Remaining work = 120 - 40 = 80 worker-days. Step 4: After hiring 4 more workers, total workers = 8 + 4 = 12. Step 5: Days needed for remaining work = 80 ÷ 12 = 6.67 days, which rounds to approximately 6⅔ days or 20/3 days.

Question 13

A worker's daily wage is ₹600. If he receives a bonus of ₹50 per day for working overtime, what will be his total earnings for 10 days including 4 days of overtime?

Accepted Answer

Step 1: Regular daily wage = ₹600. Step 2: Overtime bonus = ₹50 per day. Step 3: Regular days = 10 - 4 = 6 days. Step 4: Overtime days = 4 days. Step 5: Earnings from regular days = 600 × 6 = ₹3600. Step 6: Earnings from overtime days = (600 + 50) × 4 = 650 × 4 = ₹2600. Step 7: Total earnings = 3600 + 2600 = ₹6200.

Question 14

Two workers A and B together complete a job in 8 days. If A alone can complete the same job in 12 days, in how many days can B alone complete it?

Accepted Answer

Step 1: A's work rate = 1/12 per day. Step 2: Combined work rate of A and B = 1/8 per day. Step 3: B's work rate = 1/8 - 1/12 = (3 - 2)/24 = 1/24 per day. Step 4: B alone completes the job in 24 days.

Question 15

A and B together earn ₹3600 per month. If A earns ₹1200 per month, what is B's monthly earning?

Accepted Answer

Step 1: Combined monthly earning of A and B = ₹3600. Step 2: A's monthly earning = ₹1200. Step 3: B's monthly earning = Total earning − A's earning = 3600 − 1200 = ₹2400.

Question 16

If 15 workers can earn ₹4,500 in 6 days, how much will 10 workers earn in 9 days at the same rate of work?

Accepted Answer

Step 1: Total work-days for ₹4,500 = 15 × 6 = 90 work-days. Step 2: Earning per work-day = 4,500 ÷ 90 = ₹50 per work-day. Step 3: Work-days for 10 workers in 9 days = 10 × 9 = 90 work-days. Step 4: Total earnings = 90 × 50 = ₹4,500.

Question 17

A worker is paid ₹480 for 6 days of work. If he works for 9 days, how much total wages will he earn? Additionally, if he spends ₹150 from his earnings, what amount remains?

Accepted Answer

Step 1: Daily wage = 480 ÷ 6 = ₹80 per day. Step 2: Wages for 9 days = 80 × 9 = ₹720. Step 3: Amount remaining = 720 - 150 = ₹570.

Question 18

A contractor hires workers to complete a job. If 8 workers can finish the job in 15 days, how many workers are needed to finish the same job in 10 days, assuming all workers work at the same rate?

Accepted Answer

Step 1: Total work = 8 workers × 15 days = 120 worker-days. Step 2: For 10 days, workers needed = 120 ÷ 10 = 12 workers.

Question 19

A worker is paid ₹480 for 6 days of work. If he works for 9 days, how much total wages will he earn? Additionally, if he spends ₹120 from his earnings, what amount remains?

Accepted Answer

Step 1: Daily wage = 480 ÷ 6 = ₹80 per day. Step 2: Wages for 9 days = 80 × 9 = ₹720. Step 3: Amount remaining = 720 - 120 = ₹600.

Question 20

Two workers, P and Q, are paid wages in the ratio of their work done. P can complete a task in 8 days and Q can complete it in 12 days. They work together and complete the task in 4.8 days. If Q's wages are ₹2,400, what are P's wages?

Accepted Answer

Step 1: P's rate = 1/8, Q's rate = 1/12 per day. Step 2: Combined rate = 1/8 + 1/12 = (3+2)/24 = 5/24 per day. Step 3: Verify: Time = 1 ÷ (5/24) = 24/5 = 4.8 days ✓. Step 4: In 4.8 days, P does = 4.8 × 1/8 = 0.6 = 3/5 of work. Step 5: In 4.8 days, Q does = 4.8 × 1/12 = 0.4 = 2/5 of work. Step 6: Ratio of work P:Q = (3/5):(2/5) = 3:2. Step 7: If Q gets ₹2,400 for 2 parts, P gets (3/2) × 2,400 = ₹3,600.

Question 21

A and B together earn ₹2400 in 8 days. If A's daily wage is ₹120, what is B's daily wage?

Accepted Answer

Step 1: Combined daily wage = 2400 ÷ 8 = ₹300 per day. Step 2: A's daily wage = ₹120. Step 3: B's daily wage = 300 - 120 = ₹180 per day.

Question 22

A contractor hires workers to complete a road construction project. If 8 workers can complete the work in 15 days, how many days will 12 workers take to complete the same work, assuming all workers work at the same efficiency?

Accepted Answer

Step 1: Total work = 8 workers × 15 days = 120 worker-days. Step 2: With 12 workers, days required = 120 ÷ 12 = 10 days.

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