Time and Work Problems PDF

## Time and Work Problems 1. A can finish a work in 5 days and B can finish the same work in 8 days. If both work together and earn ₹ 6760. Find the share of A. - A can finish the work in 5 days. - B can finish the work in 8 days. - They earn ₹ 6760 together. - To find the share of A,...

## Time and Work Problems 1. A can finish a work in 5 days and B can finish the same work in 8 days. If both work together and earn ₹ 6760. Find the share of A. - A can finish the work in 5 days. - B can finish the work in 8 days. - They earn ₹ 6760 together. - To find the share of A, we need to find the ratio of their work done. - The LCM of 5 and 8 is 40. - A can complete 8/40 of the work in a day. - B can complete 5/40 of the work in a day. - The ratio of their work is 8:5. - A's share will be 8/(8 + 5) * ₹ 6760 = ₹ 4160. 2. A and B can do a piece of work in 5 days and 10 days, respectively. They began the work together but A left after some days and B finished the remaining work in 8 days. After how many days did A leave? - A can do the work in 5 days. - B can do the work in 10 days. - They work together for some days, then A leaves and B finishes the rest in 8 days. - To find how many days A worked, we need to find how much work B did in 8 days. - The LCM of 5 and 10 is 10. - A can complete 2/10 of the work in a day. - B can complete 1/10 of the work in a day. - B completed the remaining work in 8 days, so he did 8 * (1/10) = 4/5 of the work. - This means A did 1 - 4/5 = 1/5 of the work. - Since A can complete 2/10 of the work in a day, he must have worked for (1/5) / (2/10) = 1 day before leaving. 3. X and Y can do a piece of work in 45 days and 40 days respectively. They begin to work together, but X leaves after n days and then Y completes the remaining work in 23 days. What is n equal to? - X can complete the work in 45 days. - Y can complete the work in 40 days. - They work together for n days, then X leaves and Y finishes the remaining work in 23 days. - We need to find the value of n. - The LCM of 45 and 40 is 360. - X can complete 8/360 of the work in a day. - Y can complete 9/360 of the work in a day. - In n days, X completed 8n/360 of the work. - Y finished the remaining work in 23 days, which is (360 - 8n)/360 of the work. - Since Y completed the remaining work in 23 days, we can set up the equation: 23 * (9/360) = (360 - 8n)/360. - Solving for n, we get n = 9. 4. A and B together can complete a work in 1.2 days. Although A leaves after complete half of the work alone, then B alone completes the remaining half of the work. Thus it takes 2.5 days to complete the work. If B is 50% more efficient than A and B alone finished the whole work, then how many days will he take? - A and B can complete the work in 1.2 days together. - A does half the work alone, then B does the other half. - It takes 2.5 days to complete the work. - B is 50% more efficient than A. - We need to find how many days B would take to complete the work alone. - First, let's figure out how much work A does in 1 day. Since they complete the work in 1.2 days together, A does 1/(1.2) = 5/6 of the work in 1 day. - We know A completes half the work before leaving, so it takes him 1/(5/6) = 1.2 days to complete half the work. - Since B completes the other half of the work in 2.5 days, and A had already done half the work, we can assume B completed his half of the job in 2.5 - 1.2 = 1.3 days. - As B is 50% more efficient than A, B can do 1.5 times more work than A in the same amount of time. - Therefore, if B were to work on the entire job alone, it would take him 1.3 days * (2/1.5) = 1.73 days (approximately) to finish the work. 5. A alone can complete a work in 10 days and B can complete it in 15 days. A and B undertake the work for ₹ 4800. With the help of C, they complete the work in 5 days. What amount is to be paid to C? - A can complete the work in 10 days. - B can complete the work in 15 days. - They take on the work for ₹ 4800. - They finish the work in 5 days with the help of C. - We need to find C's share. - First, find the LCM of 10, 15, and 5 which is 30. - A can do 3 units of work per day (30/10 = 3). - B can do 2 units of work per day (30/15 = 2). - Together, they can do 5 units of work per day (3 + 2 = 5). - In 5 days, with C, they complete 15 units of work (5 days * 3 units per day = 15 units). - Since A and B can do 5 units per day, C must have completed 10 units of work (15 - 5 = 10). - The ratio of their work is 3:2:10. - This means C is responsible for 10/15 of the work. - C’s share will be (10/15) * ₹ 4800 = ₹ 3200. 6. Raja and Rocky together can complete painting work in 5 days. Together they both start painting, but after 2 days, Rocky falls sick and leaves the work. If Raja completes the remaining painting in 4 days, find the number of days in which Rocky alone can do the work. - Raja and Rocky can complete the work in 5 days together. - They work for 2 days together, then Rocky leaves and Raja finishes the rest in 4 days. - We need to find out how many days Rocky would take alone. - Let's assume Raja can complete the work in 'x' days and Rocky in 'y' days. - In 1 day, Raja can complete 1/x of the work. - In 1 day, Rocky can complete 1/y of the work. - Together, they complete 1/5 of the work per day (1/x + 1/y = 1/5). - They work together for 2 days so they complete 2/5 of the work in 2 days. - Raja then finishes the remaining 3/5 of the work in 4 days. Therefore, Raja can complete 3/20 of the work in one day. - We can now set up the equation: 1/x = 3/20. This means Raja takes 20/3 days to complete the work alone. - Now we can plug this value back into our initial equation (1/x + 1/y = 1/5): 3/20 + 1/y = 1/5. - Solving for y, we get y = 12. - Therefore, Rocky can complete the work in 12 days alone. 7. A and B together can complete a work in 35 days. If A works alone and completes 4/7 of the work and left the remaining work for B. Thus if it takes 114 days to complete the work. So how many days will A who is more efficient in both, complete the work alone? - A and B together finish the work in 35 days. - A completes 4/7 of the work, leaving the rest for B. - The entire work is finished in 114 days. - We need to find how many days it takes A to complete the work alone. - Let's assume A takes ‘x’ days to complete the work alone. - In 1 day, A completes 1/x of the work. - In 35 days, A and B complete 1 unit of work together, so in one day, they complete 1/35 of the work. - We know that A completes 4/7 of the work in 114 days. - This means in 1 day, A completes (4/7) / 114 = 1/199.5 of the work. - We can now set up the equation: 1/x = 1/199.5 - Solving for x, we get x = 199.5. - Therefore, A can complete the entire work alone in 199.5 days. 8. Anil can paint a house in 12 days, while Barun can paint it in 16 days. Anil, Barun and Chandu undertaken to paint the house for 24000 and the three of them together complete the painting in 6 days. If Chandu is paid in proportion to the work done by him, then the amount in received by him is- - Anil takes 12 days, Barun takes 16 days. - They work together and finish in 6 days. - The total payment is ₹ 24000. - We need to determine Chandu's share based on his contribution. - First, we find the LCM of their individual times: 12, 16, and 6 - the LCM is 48. - This means Anil can paint 4 units in a day (48/12 = 4). - Barun can paint 3 units in a day (48/16 = 3). - Together (Anil + Barun), they can paint 7 units in a day. - In 6 days, they can paint 42 units (6 * 7 = 42) while they are painting the house. - Overall, to paint the entire house, 48 units are needed. - This means Chandu contributed 6 units to the work (48 - 42 = 6). - His share is therefore 6/48 * ₹ 24000 = ₹ 3000. 9. A, B and C can independently do a work in 15 days, 20 days and 30 days, repectively. They work together for some time after which C leaves. Total of 18000 is paid for the work and B gets 6000 more than C. For how many days did A work? - A, B, and C work independently in 15, 20, and 30 days. - They work together then C leaves. - The total payment is ₹ 18000. - B earns ₹ 6000 more than C. - We need to find how many days A worked. - The LCM of 15, 20, and 30 is 60. - A completes 4/60 of the work in a day. - B completes 3/60 of the work in a day. - C completes 2/60 of the work in a day. - Let's say A worked for 'x' days. - Their combined work would be (4x/60) + (3x/60) + (2x/60) = 9x/60 - B's earnings are ₹ 6000 more than C's, meaning the difference in their work is 6000 / (9x/60) = 40000/3x. - The difference in work done by B and C in one day is 1/20. - Therefore, we can set up the equation: (40000/3x) = 1/20 - Solving for x, we get x = 8 - So, A worked for 8 days. 10. A and B undertake a project worth ₹ 36,000. A alone can do the work in 25 days. They worked together for 5 days. For the next five days, B worked alone. After that, A substituted B and completed the remaining work in 5 days. The share of A in the earnings is: - A and B take on a ₹ 36,000 project. - A can complete the work in 25 days. - They work together for 5 days, then B continues for 5 days, and A finishes the rest in 5 days. - We need to find A's share of the earnings. - The LCM of 25 and 5 is 25. - A can complete 1 unit of work in a day (25/25 = 1). - B can complete 5 units of work in a day (25/5 = 5). - In 5 days, they complete 30 units together (5 * (1 + 5) = 30) - B works for the next 5 days, completing 25 units of work (5 * 5 = 25) - A then completes the remaining 5 units in 5 days (25 * 1 = 5). - In total, 60 units represent the whole project (30 + 25 + 5 = 60). - A completed 10 units (5 + 5) which means A deserves 10/60 * ₹ 36000 = ₹ 6000. 11. Samir and Puneet can complete the same work in 10 days and 15 days respectively. The work was assigned for ₹ 4500. After working together for 3 days Samir and Puneet involved Ashok. The work was completed in total 5 days. What amount (in ₹) was paid to Ashok? - Samir can do the work in 10 days. - Puneet can do the work in 15 days. - The work was assigned for ₹ 4500. - They work together for 3 days, then Ashok joins and the work is completed in 5 days total. - We need to find Ashok's share of the payment. - The LCM of 10 and 15 is 30. - Samir can complete 3 units per day (30/10 = 3). - Puneet can complete 2 units per day (30/15 = 2) - In the first 3 days, together, they complete 15 units of work (3 * (3 + 2) = 15). - As the work was completed in 5 days, they completed 30 units of work in total. - That means, Ashok contributed 15 units of work (30 - 15 = 15). - So, Ashok’s share is 15/30 * ₹ 4500 = ₹ 2250. 12. Sachin alone can complete a piece of work for ₹8500 in 8.5 days. But with the help of Vishnu the work is completed in 6 days. The share to be paid Vishnu? - Sachin can complete the work in 8.5 days. - The work costs ₹ 8500. - With Vishnu, they finish in 6 days. - We need to find Vishnu’s share. - The LCM of 8.5 and 6 is 102. - In one day, Sachin can complete 102/8.5 = 12 units of work. - In 6 days, Sachin would’ve completed 72 units of work (6 * 12 = 72). - The work is completed in 6 days, so Vishnu must have completed 30 units of work (102 - 72 = 30) - Vishnu’s share will be 30/ 102 * ₹ 8500 = ₹ 2500. ## Important Notes: - Efficiency is directly proportional to the work done and inversely proportional to the time taken. - If two workers are able to do a job in x and y days respectively, then they can complete the work in xy/(x+y) days. - If two workers are working together and one leaves after some time, the remaining work is completed by the second worker in the remaining days. - It is important to note that the share received by a worker is directly proportional to the efficiency of each worker. - The work done by two workers can be divided, while the amount earned for the work cannot be divided as it is a common benefit. I hope this helps!