Question 1

If 5 workers can paint a wall in 8 hours, how many workers are needed to paint the same wall in 4 hours?

Accepted Answer

Step 1: Total work = 5 workers × 8 hours = 40 worker-hours. Step 2: To complete in 4 hours, workers needed = 40 ÷ 4 = 10 workers.

Question 2

A's work efficiency is twice that of B. If A can complete a job in 9 days, in how many days can B complete the same job?

Accepted Answer

Step 1: Let B's efficiency = x. Then A's efficiency = 2x. Step 2: A completes work in 9 days, so 2x × 9 = 1 (total work). Step 3: Therefore, 2x = 1/9, which means x = 1/18. Step 4: B's time = 1 ÷ (1/18) = 18 days.

Question 3

If 5 workers can build a wall in 20 days, how many days will 10 workers take to build the same wall?

Accepted Answer

Step 1: Total work = 5 workers × 20 days = 100 worker-days. Step 2: With 10 workers, days required = 100 worker-days ÷ 10 workers = 10 days. Therefore, 10 workers will take 10 days.

Question 4

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 5

A man is paid ₹15 per hour. If he works 6 hours a day for 5 days, what is his total earnings?

Accepted Answer

Step 1: Hourly wage = ₹15. Step 2: Hours per day = 6. Step 3: Number of days = 5. Step 4: Total hours worked = 6 × 5 = 30 hours. Step 5: Total earnings = 15 × 30 = ₹450.

Question 6

A worker completes 1/4 of a job in 5 days. At this rate, how many days will it take to complete the entire job?

Accepted Answer

Step 1: Worker completes 1/4 of the job in 5 days. Step 2: To complete the entire job (4/4), time needed = 5 × 4 = 20 days.

Question 7

A and B together earn ₹1200 per day. If A earns ₹700 per day, how much does B earn per day?

Accepted Answer

Step 1: Combined daily earnings of A and B = ₹1200. Step 2: A's daily earnings = ₹700. Step 3: B's daily earnings = 1200 − 700 = ₹500.

Question 8

A can do 1/3 of a work in 5 days. In how many days can A complete the entire work?

Accepted Answer

Step 1: A completes 1/3 work in 5 days. Step 2: To complete the full work (3/3), A needs 5 × 3 = 15 days.

Question 9

If 8 men can build a wall in 15 days, how many days will 12 men take to build the same wall?

Accepted Answer

Step 1: Total work = 8 men × 15 days = 120 man-days. Step 2: With 12 men, days needed = 120 ÷ 12 = 10 days.

Question 10

A pipe can empty a full cistern in 8 hours. What fraction of the cistern will it empty in 3 hours?

Accepted Answer

Step 1: Work done by pipe in 1 hour = 1/8 of the cistern. Step 2: Work done in 3 hours = 3 × (1/8) = 3/8 of the cistern.

Question 11

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

Accepted Answer

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

Question 12

Two workers, M and N, working together can complete a job in 6 days. If M works alone, he takes 9 days more than N. How many days does N take to complete the job alone?

Accepted Answer

Step 1: Let N take x days. Then M takes (x + 9) days. Step 2: Combined rate: 1/x + 1/(x+9) = 1/6. Step 3: Multiply through by 6x(x+9): 6(x+9) + 6x = x(x+9). Step 4: 6x + 54 + 6x = x² + 9x. Step 5: x² + 9x - 12x - 54 = 0 → x² - 3x - 54 = 0. Step 6: (x - 9)(x + 6) = 0. Step 7: x = 9 (reject x = -6). Therefore, N takes 9 days.

Question 13

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 14

A task requires 120 worker-days to complete. If 5 workers start the task and after 12 days, 3 more workers join them, how many more days are needed to complete the task?

Accepted Answer

Step 1: Calculate work completed in first 12 days. Work done = 5 workers × 12 days = 60 worker-days. Step 2: Calculate remaining work. Remaining work = 120 - 60 = 60 worker-days. Step 3: Calculate new workforce. New workforce = 5 + 3 = 8 workers. Step 4: Calculate days needed. Days needed = 60 worker-days ÷ 8 workers = 7.5 days.

Question 15

Two workers are paid wages in the ratio 5:3. If the worker with higher wage earns ₹2,500 per month, and they complete a project together in 8 days earning ₹9,600 total, what is the daily wage of the lower-paid worker?

Accepted Answer

Step 1: Wage ratio is 5:3. Higher-paid worker earns ₹2,500 per month. Let higher wage = 5x, lower wage = 3x. Step 2: 5x = 2,500, so x = 500. Lower wage = 3 × 500 = ₹1,500 per month. Step 3: Daily wage of lower-paid worker = 1,500 ÷ 30 = ₹50 per day.

Question 16

A contractor hires workers to complete a task. If 6 workers can finish the work in 9 days, how many days will 4 workers take to complete the same work, assuming all workers work at the same rate?

Accepted Answer

Step 1: Calculate total work in worker-days. Total work = 6 workers × 9 days = 54 worker-days. Step 2: With 4 workers, days required = Total work ÷ Number of workers = 54 ÷ 4 = 13.5 days.

Question 17

A and B work together and earn ₹7,200 for a project. A works for 8 days and B works for 6 days. If A's daily wage is ₹600, what is B's daily wage?

Accepted Answer

Step 1: Calculate A's total earnings. A's earnings = 8 days × ₹600/day = ₹4,800. Step 2: Calculate B's total earnings. B's earnings = Total payment - A's earnings = ₹7,200 - ₹4,800 = ₹2,400. Step 3: Calculate B's daily wage. B's daily wage = ₹2,400 ÷ 6 days = ₹400/day.

SSC MTS Time & Work Questions

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