Examples and Practice Questions (1 to 5)
Type 1
Question 1: Kalyani and Anil together can do a job in 18 days. Kalyani can do the same job alone in 36 days. How long will Anil take to complete the job when working alone?
Step 1: Divide the Total Work in Parts by taking LCM.
LCM of 18 and 36 is 420. This is the total number of parts in which we have divided our work.
Step 2: Calculate Parts of Work Done by Each Person or Group.
Kalyani and Anil take 18 days to do the work together. So, they will do \(36/18\) parts or 2 parts of the work in 1 day.
Kalyani takes 36 days to do the work. So, she will do \(36/36\) part or 1 part of the work in 1 day.
Step 3: Calculate Parts of Work Done by Given Person.
Kalyani and Anil do 2 parts of the work in 1 day. Kalyani alone does 1 part of the work in 1 day. So, Anil alone will do
(Kalyani and Anil) – Kalyani = 2 – 1 = 1 part of the work in 1 day.
Step 4: Calculate Total Time to do Work.
Anil completes 1 part of the work in 1 day. This means that he will complete the whole work in \(36/1\) days or 36 days.
Final Answer: 36 Days.
Question 2: Arti and Arushi together can do a job in 12 days. Arti can do the same job alone in 30 days. How long will Arushi take to complete the job when working alone?
Step 1: Divide the Total Work in Parts by taking LCM.
LCM of 12 and 30 is 60. This is the total number of parts in which we have divided our work.
Step 2: Calculate Parts of Work Done by Each Person or Group.
Arti and Arushi take 12 days to do the work together. So, they will do \(60/12\) parts or 5 parts of the work in 1 day.
Arti takes 30 days to do the work. So, she will do \(60/30\) parts or 2 parts of the work in 1 day.
Step 3: Calculate Parts of Work Done by Given Person.
Arti and Arushi do 5 parts of the work in 1 day. Arti alone does 2 parts of the work in 1 day. So, Arushi alone will do
(Arti and Arushi) – Arti = 5 – 2 = 3 parts of the work in 1 day.
Step 4: Calculate Total Time to do Work.
Arushi completes 3 part of the work in 1 day. This means that she will complete the whole work in \(60/3\) days or 20 days.
Final Answer: 20 Days.
Practice Questions
Anurag and Manu together can do a job in 15 days. Anurag can do the same job alone in 40 days. How long will Manu take to complete the job when working alone?
Jatin and Yash together can do a job in 17 days. Jatin can do the same job alone in 34 days. How long will Yash take to complete the job when working alone?
Kavya and Manisha together can do a job in 19 days. Kavya can do the same job alone in 38 days. How long will Manisha take to complete the job when working alone?
Deepak and Rohan together can do a job in 18 days. Deepak can do the same job alone in 45 days. How long will Rohan take to complete the job when working alone?
Aryan and Dhruv together can do a job in 9 days. Aryan can do the same job alone in 18 days. How long will Dhruv take to complete the job when working alone?
Type 2
Question 3: Kamalika can do a piece of work in 49 days and Karan in 35 days. They work together for 5 days and then Karan left. Find out the time taken by Kamalika to finish the remaining work.
Step 1: Divide the Total Work in Parts by taking LCM.
LCM of 49 and 35 is 245. This is the total number of parts in which we have divided our work.
Step 2: Calculate Parts of Work Done by Each Person or Group.
Kamalika takes 49 days to do the work. So, she will do \(245/49\) parts or 5 parts of the work in 1 day.
Karan takes 35 days to do the work. So, he will do \(245/35\) parts or 7 parts of the work in 1 day.
Step 3: Calculate Total Work Left to be Done.
Kamalika and Karan together do 5 + 7 parts or 12 parts of the work in 1 day. In 5 days, they will complete 12*5 or 60 parts of the work.
Work left to be done now is 245 – 60 parts or 185 parts.
Step 4: Calculate Total Time to do Work.
Kamalika completes 5 parts of the work in 1 day. This means that she will complete the remaining work in \(185/5\) days or 37 days.
Final Answer: 37 Days.
Question 4: Avinash can do a piece of work in 28 days and Nitin in 16 days. They work together for 4 days and then Nitin left. Find out the time taken by Avinash to finish the remaining work.
Step 1: Divide the Total Work in Parts by taking LCM.
LCM of 28 and 16 is 112. This is the total number of parts in which we have divided our work.
Step 2: Calculate Parts of Work Done by Each Person or Group.
Avinash takes 28 days to do the work. So, he will do \(112/28\) parts or 4 parts of the work in 1 day.
Nitin takes 16 days to do the work. So, he will do \(112/16\) parts or 7 parts of the work in 1 day.
Step 3: Calculate Total Work Left to be Done.
Avinash and Nitin together do 4 + 7 parts or 11 parts of the work in 1 day. In 4 days, they will complete 11*4 or 44 parts of the work.
Work left to be done now is 112 – 44 parts or 68 parts.
Step 4: Calculate Total Time to do Work.
Avinash completes 4 parts of the work in 1 day. This means that he will complete the remaining work in \(68/4\) days or 17 days.
Final Answer: 17 Days.
Practice Questions
Sanchit can do a piece of work in 40 days and Kalyani in 24 days. They work together for 6 days and then Kalyani left. Find out the time taken by Sanchit to finish the remaining work.
Mahesh can do a piece of work in 28 days and Arun in 20 days. They work together for 5 days and then Arun left. Find out the time taken by Mahesh to finish the remaining work.
Anish can do a piece of work in 39 days and John in 26 days. They work together for 6 days and then John left. Find out the time taken by Anish to finish the remaining work.
Girish can do a piece of work in 48 days and Katherine in 16 days. They work together for 4 days and then Katherine left. Find out the time taken by Girish to finish the remaining work.
Shivam can do a piece of work in 40 days and Nikita in 32 days. They work together for 8 days and then Nikita left. Find out the time taken by Shivam to finish the remaining work.
Type 3
Question 5: Rashi can do a piece of work in 40 days and Abhishek can do it in 24 days. In how many days will they finish the work, both working together?
Step 1: Divide the Total Work in Parts by taking LCM.
LCM of 40 and 24 is 120. This is the total number of parts in which we have divided our work.
Step 2: Calculate Parts of Work Done Together.
Rashi takes 40 days to do the work. So, she will do \(120/40\) parts or 3 parts of the work in 1 day.
Abhishek takes 24 days to do the work. So, he will do \(120/24\) parts or 5 parts of the work in 1 day.
Rashi and Abhishek do 3 + 5 parts or 8 parts of the work in 1 day.
Step 3: Calculate Total Time to do Work.
The total work has 120 parts. This means that they will complete the whole work in \(120/8\) days or 15 days.
Final Answer: 15 Days.
Question 6: Papu can do a piece of work in 45 days and Siya can do it in 36 days. In how many days will they finish the work, both working together?
Step 1: Divide the Total Work in Parts by taking LCM.
LCM of 45 and 36 is 180. This is the total number of parts in which we have divided our work.
Step 2: Calculate Parts of Work Done Together.
Papu takes 45 days to do the work. So, he will do \(180/45\) parts or 4 parts of the work in 1 day.
Siya takes 36 days to do the work. So, he will do \(180/36\) parts or 5 parts of the work in 1 day.
Papu and Siya do 4 + 5 parts or 9 parts of the work in 1 day.
Step 3: Calculate Total Time to do Work.
The total work has 180 parts. This means that they will complete the whole work in \(180/9\) days or 20 days.
Final Answer: 20 Days.
Practice Questions
Anthony can do a piece of work in 30 days and Anubhav can do it in 20 days. In how many days will they finish the work, both working together?
Tanvi can do a piece of work in 24 days and Bharti can do it in 40 days. In how many days will they finish the work, both working together?
Sunil can do a piece of work in 21 days and Nishi can do it in 28 days. In how many days will they finish the work, both working together?
Vani can do a piece of work in 48 days and Neeraj can do it in 16 days. In how many days will they finish the work, both working together?
Ajeet can do a piece of work in 30 days and Shivam can do it in 15 days. In how many days will they finish the work, both working together?
Type 4
Question 7: Yash can do a piece of work in 24 days. He worked at it for 6 days and Siddharth finished the remaining work in 12 days. How long will Siddharth take to do the whole work alone?
Step 1: Divide the Total Work in Parts.
Yash completes the whole work in 24 days. So, we will assume that the work has 24 parts.
Step 2: Calculate Work Left After Given Days.
Yash works for 6 days. This means that he completed 6 parts of the work.
Work left to be done now is 24 – 6 parts or 18 parts.
Step 3: Calculate Work Done by Other Person in One Day.
Siddharth completes 18 parts of the work in 12 days. This means that he will complete \(18/12\) parts of \(3/2\) parts of the work in 1 day.
Step 4: Calculate Time taken to do complete work.
Total work is 24 parts and Siddharth completes \(3/2\) parts in 1 day. This means that he will complete thw whole work in \(24*2/3\) days or 16 days.
Final Answer: 16 Days.
Question 8: Vaibhav can do a piece of work in 38 days. He worked at it for 12 days and James finished the remaining work in 13 days. How long will James take to do the whole work alone?
Step 1: Divide the Total Work in Parts.
Vaibhav completes the whole work in 38 days. So, we will assume that the work has 38 parts.
Step 2: Calculate Work Left After Given Days.
Vaibhav works for 12 days. This means that he completed 12 parts of the work.
Work left to be done now is 38 – 12 parts or 26 parts.
Step 3: Calculate Work Done by Other Person in One Day.
James completes 26 parts of the work in 13 days. This means that he will complete \(26/13\) parts of 2 parts of the work in 1 day.
Step 4: Calculate Time taken to do complete work.
Total work is 38 parts and James completes 2 parts in 1 day. This means that he will complete thw whole work in \(38/2\) days or 19 days.
Final Answer: 19 Days.
Practice Questions
Rohit can do a piece of work in 44 days. He worked at it for 8 days and Shashank finished the remaining work in 9 days. How long will Shashank take to do the whole work alone?
Shivam can do a piece of work in 45 days. He worked at it for 15 days and Jatin finished the remaining work in 22 days. How long will Jatin take to do the whole work alone?
Soham can do a piece of work in 45 days. He worked at it for 6 days and Deep finished the remaining work in 13 days. How long will Deep take to do the whole work alone?
Akash can do a piece of work in 30 days. He worked at it for 15 days and Sanchit finished the remaining work in 8 days. How long will Sanchit take to do the whole work alone?
Dinesh can do a piece of work in 36 days. He worked at it for 14 days and Jay finished the remaining work in 11 days. How long will Jay take to do the whole work alone?
Type 5
Question 9: While working 7 hours a day, Abhinav alone can complete a piece of work in 18 days and John alone in 45 days. In what time would they complete it together, working 6 hours a day?
Step 1: Divide the Total Work in Parts by taking LCM..
LCM of 18 and 45 will be 90. This is the total number of parts in which we have divided our work.
Step 2: Calculate Parts of Work Done by Each Person.
Abhinav takes 18 days to do the whole work. So, he will do \(90/18\) parts or 5 parts of the work in 1 day.
John takes 45 days to do the whole work. So, he will do \(90/45\) part or 2 parts of the work in 1 day.
Step 3: Calculate Time Taken to do Work.
Abhinav and John complete 5 + 2 parts or 7 parts of the work in 1 day. This means that they will complete the whole work in \(90/7\) days.
We have to convert days into hours. Abhinav and John work 7 hours per day. So, they will work 7*\(90/7\) hours or 90 hours to complete the work.
Step 4: Calculate the Time Taken for New Hours.
Total work is completed in 90 hours. If Abhinav and John work for 6 hours per day, they will complete it in \(90/6\) days or 15 days.
Final Answer: 15 Days.
Question 10: While working 10 hours a day, Ira alone can complete a piece of work in 18 days and Anushri alone in 27 days. In what time would they complete it together, working 9 hours a day?
Step 1: Divide the Total Work in Parts by taking LCM..
LCM of 18 and 27 will be 54. This is the total number of parts in which we have divided our work.
Step 2: Calculate Parts of Work Done by Each Person.
Ira takes 18 days to do the whole work. So, she will do \(54/18\) parts or 3 parts of the work in 1 day.
Anushri takes 27 days to do the whole work. So, she will do \(54/27\) part or 2 parts of the work in 1 day.
Step 3: Calculate Time Taken to do Work.
Ira and Anushri complete 3 + 2 parts or 5 parts of the work in 1 day. This means that they will complete the whole work in \(54/5\) days.
We have to convert days into hours. Ira and Anushri work 10 hours per day. So, they will work 10*\(54/5\) hours or 108 hours to complete the work.
Step 4: Calculate the Time Taken for New Hours.
Total work is completed in 108 hours. If Ira and Anushri work for 9 hours per day, they will complete it in \(108/9\) days or 12 days.
Practice Questions
Final Answer: 12 Days.
Suresh and Tanvi can do a work in 16 and 32 days respectively. They worked together for 7 days and then Suresh left. How long did Tanvi take to complete the remaining work?
While working 9 hours a day, Vikas alone can complete a piece of work in 45 days and Ananya alone in 36 days. In what time would they complete it together, working 5 hours a day?
While working 10 hours a day, Rishabh alone can complete a piece of work in 25 days and Kritika alone in 25 days. In what time would they complete it together, working 5 hours a day?
While working 9 hours a day, Anurag alone can complete a piece of work in 35 days and Ajit alone in 40 days. In what time would they complete it together, working 8 hours a day?
While working 6 hours a day, Rajeev alone can complete a piece of work in 35 days and Raj alone in 40 days. In what time would they complete it together, working 8 hours a day?
While working 9 hours a day, Akansha alone can complete a piece of work in 39 days and Mayur alone in 42 days. In what time would they complete it together, working 7 hours a day?