Bissoy.com
Doctors Medicines MCQs Q&A

Ratul and Praful together can complete a task in 18 days. They start the task together, but Ratul had to leave 7 days before the work got over. As a result it took a total of 23 days to complete the task. How many days would it have taken Pratul to complete the work by himself?

Ratul and Praful together can complete a task in 18 days. They start the task together, but Ratul had to leave 7 days before the work got over. As a result it took a total of 23 days to complete the task. How many days would it have taken Pratul to complete the work by himself? Correct Answer 63

Short Trick∶

Let the efficiency of Ratul be R and efficiency of Pratul be P, then

Total work = (R + P) × 18 = 18R + 18P      ----(1)

Total work when Ratul did only 16 days and Pratul did 23 days.

Total work = 16R + 23P      ----(2)

From equation (1) and equation (2)

⇒ 18R + 18P = 16R + 23P

⇒ 2R = 5P

Efficiency ratio of R to P = 5 ∶ 2

Total work = 18 × 5 + 18 × 2 = 18 × 7 = 126

Pratul alone can complete the whole work in = 126/2 = 63 days

Details solution∶

Suppose Ratul complete the whole work in = x days

Suppose Pratul complete the whole work in = y days

Ratul completes in 1 day = 1/x work

Pratul completes in 1 day = 1/y work

⇒ 18 × (1/x + 1/y) = 1

⇒ 1/x + 1/y = 1/18      ----(1)

Ratul did the work only = 23 – 7 = 16 days

Pratul did the remaining work = 23 days

⇒ 16/x + 23/y = 1      ----(2)

Multiply by 16 in equation (1) and subtract from equation (2)

⇒ 16x + 23/y – 16/x – 16/y = 1 – 16/18

⇒ 7/y = 1/9

⇒ 1/y = 1/(9 × 7) = 1/63

Pratul complete the whole task in 63 days.

Related Questions

Rathin & Bratin together can complete a piece of work in 12 days. They start the work together but Rathin had to leave 5 days before the work got over. As a result it took a total of 15 days to complete the work. How many days would it have taken Bratin to complete the work by himself?
A and B can complete a task in 12 days. However, A had to leave a few days before the task was completed and hence it took 16 days in all to complete the task. If A alone could complete the work in 21 days, how many days before the work getting over did A leave?
A and B can complete a task in 18 days. However, A had to leave a few days before the task was completed and hence it took 27 days in all to complete the task. If A alone could complete the work in 21 days, how many days before the work getting over did A leave?
A and B can complete a task in 1.5 days. However, A had to leave a few days before the task was completed and hence it took 2 days in all to complete the task. If A alone could complete the work in 2.625 days, how many days before the work getting over did A leave?
A and B can complete a task in 1.5 days. However, A had to leave a few days before the task wascompleted and hence it took 2 days in all to complete the task. If A alone could complete the work in2.625 days, how many days before the work getting over did A leave?
In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: A can do a piece of work in 10 days and B can do the same work in 15 days. They start working together and after 4 days, A left the work. Find in how many days the total work will be completed. Quantity B: P can do a piece of work in 15 days and Q can do the same work in 25 days. They start working together and after 5 days, Q left the work. Find in how many days the remaining work will gets completed.
Newton, Einstein, and Tesla working alone can do a piece of work in 20, 30, and 60 days respectively. All three of them start the work together, but after x days Newton leaves and then after y more days Einstein leaves and Tesla completes the remaining work. If Einstein had not left, Tesla and Einstein would have completed the remaining work in (y + 6) days after Newton had left. If both Newton and Einstein had stayed, the work would have been completed in (x + 6) days. What is the total number of days taken to complete the work?
In a survey of 25 students, it was found that 15 had taken Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects. Find the number of students who had taken both Physics and Chemistry but not Mathematics.
Each of the question below consists of a question and three statements number I, II and III given below it. You have to decide whether the data provided in the statement are sufficient to answer the question. Two person X and Y together can make 25% of total number of bricks in 4.8 days. Another person Z can make 50 bricks in a day. What is the time taken by person X and Z together to make the total number of bricks? I. Dimensions of a brick is (3cm × 4cm × 5cm) while the dimension of a cuboids when all the bricks are put together is (72cm × 80cm × 50cm) and ratio of number of days taken by X and Y alone to make the total number of bricks is 3 : 2. II. The total number of bricks is 4800 and person Y can make 150 bricks in day. III. Total volume of all the bricks together is 1.008m3 and dimension of a bricks is (5cm × 6cm × 7cm) and time taken by Z to make total number of bricks is 200 % more than the total time taken by person Y to make total number of bricks.
A and B can complete a work in 36 days. However, A had to leave a few days before the work was completed and hence it took 54 days to complete the work. If A alone can complete a work in 48 days, then how many days before the completion of the work did A take leave?