Time and Work Questions

• Two inlet pipes A and B can fill a tank in 40 minutes and 60 minutes, respectively. An outlet pipe C empties the tank. With all three pipes open together, the tank fills in 30 minutes. How long would C alone take to empty a full tank?
• Two conveyor belts deliver baggage at constant rates. Belt 1 delivers 3 tonnes in 5 minutes; Belt 2 delivers 1 tonne in 2 minutes. If both belts run together, how long will it take to deliver 33 tonnes?
• Rohit, Harsh, and Sanjeev are typists who together type 216 pages in 4 hours (working simultaneously). In one hour, Sanjeev exceeds Harsh by as many pages as Harsh exceeds Rohit. Over 5 hours, Sanjeev types as many pages as Rohit does in 7 hours. How many pages per hour do Rohit, Harsh, and Sanjeev type, respectively?
• A and B together can complete a work in 12 days; B and C together can complete it in 16 days. A works alone for 5 days; B works alone for 7 days; then C works alone and finishes the job in 13 days. In how many days can C alone complete the entire work?
• A and B together can complete a work in 12 days; B and C together can complete it in 15 days. The job is done sequentially: A works alone for 3 days, then B alone for 8 days, then C alone for 10 days to finish it. In how many days can C alone complete the entire work?
• A supplies 20 men who work 8 hours per day for 6 days. B supplies 15 men working 9 hours per day for 7 days. C supplies 10 men working 6 hours per day for 8 days. If ₹ 636 is paid for all the labour, what is C's share?
• A and B can do a piece of work in 45 days and 40 days, respectively. They start together, but A leaves after some days. B then completes the remaining work alone in 23 days. After how many days from the start did A leave?
• Either 50 men or 80 women can finish a job in 50 days (equal total work). A contractor employs 40 men and 48 women. After every 10 days, 5 men and 8 women are removed, and this pattern continues until the job is completed. In how many days is the work finished?
• A can complete a job in 10 days and B in 15 days. They work together for 5 days; the remaining work is finished by C in 2 more days. If the total wage for the job is Rs 3000 and payment is proportional to work done, what are the daily wages of A, B, and C, respectively?
• Asha is 25% more efficient than Usha. Usha takes 25 days to complete a piece of work alone. Asha starts the work alone; Usha joins her exactly 5 days before completion. For how many days did Asha work alone?
• Krishna can do a work in 10 days; Mohan can do the same in 20 days. They start together; after 3 days Krishna leaves and Mohan finishes the job alone. By how many days did Mohan's solo work exceed the total time that would have been required if both had worked together for the entire job?
• Time and Work – Three workers with staggered start: Kareena can complete the entire work in 9 days, while Krishna alone needs 18 days. They both start together and work for the first 3 days. After that, Shahid joins them; he can finish the whole work alone in 3 days. Calculate the total number of days required for the three of them to complete the work under this schedule.
• Time and Work – Staggered departures: Kavita, Babita, and Samita start a job together. Samita leaves after the first 5 days, and Babita leaves after completing 8 days of work in total. Individually, their times to finish the entire work alone are: Kavita 20 days, Babita 60 days, and Samita 30 days. After these departures, in how many additional days will Kavita alone complete the remaining work?
• Work and Consumption – Mid-Day Meal planning: Food stocks are sufficient for 250 students for 33 days when each student receives 125 g per day. If 80 more students join (total 330) and the per-student serving remains 125 g, for how many days will the food last?
• Inverse Variation – Changing workforce: A certain number of men can complete a job in 80 days. If there were 10 fewer men, the job would require 20 additional days (i.e., 100 days). How many men were there initially?
• Combined rates – Three workers together: A can complete the work in 8 days, B in 10 days, and C in 20 days. If all three work together from the start, in how many days will the work be completed?
• Increasing workforce in steps: 15 men could finish a piece of work in 210 days at the original staffing. However, at the end of every 10 days, 15 additional men are employed (i.e., workforce grows by +15 after each 10-day block). How many days will it now take to finish the work?
• Finding a partner’s rate from partial collaboration: Ramesh can finish a job in 20 days. He works alone for 10 days, then completes the remaining work in 2 additional days working together with Dinesh. In how many days would Ramesh and Dinesh together complete the whole job from the start?
• Back-solving individual time from staggered completion: A and B together can finish a work in 30 days. They work together for 20 days, after which B leaves. A alone completes the remaining work in 20 more days. Find the time in which A alone can complete the whole work.
• Inferring individual time from modified efficiencies: Two workers A and B together complete a job in 5 days. If A worked at twice his actual efficiency and B worked at one-third of his actual efficiency, the job would be done in 3 days. How long would A alone take to complete the job at his actual efficiency?