Examples and Practice Questions (11 to 15)
Type 11
Question 1: Shashank and Abdul together can complete a work in 24 days. They start together. But, after 11 days, Abdul left the work. If the work is completed after 21 more days, how long will Abdul alone take to do the work?
Step 1: Divide the Total Work in Parts.
Shashank and Abdul complete the whole work together in 24 days. So, we will assume that the work has 24 parts. This means that they both complete 1 part of the work in 1 day.
Step 2: Calculate Work Left After Given Days.
They work together for 11 days. This means that they completed 11 parts of the work.
Work left to be done now is 24 – 11 parts or 13 parts.
Step 3: Calculate Work Done by Other Person in One Day.
Sashank completes 13 parts of the work in 21 days. This means that he will complete \(13/21\) parts of the work in 1 day.
Step 4: Calculate Time taken to do complete work Alone.
In step 1, we decided that Shashank + Abdul do 1 part of work in 1 day. In step 3, we calculated that Sashank complete \(13/21\) parts of the work in 1 day. This means that,
Shashank + Abdul = 1 and Sashank = \(13/21\)
Abdul = 1 – Shashank or 1 – \(13/21\) or \(8/21\) parts.
Abdul completes \(8/21\) parts of the work in 1 day. The total work is 24 parts. Therefore, he will complete the whole work in \((24*21)/8\) days or 63 days.
Final Answer: 63 Days.
Question 2: Divya and Rakesh together can complete a work in 24 days. They start together. But, after 16 days, Rakesh left the work. If the work is completed after 14 more days, how long will Rakesh alone take to do the work?
Step 1: Divide the Total Work in Parts.
Divya and Rakesh complete the whole work together in 24 days. So, we will assume that the work has 24 parts. This means that they both complete 1 part of the work in 1 day.
Step 2: Calculate Work Left After Given Days.
They work together for 16 days. This means that they completed 16 parts of the work.
Work left to be done now is 24 – 16 parts or 8 parts.
Step 3: Calculate Work Done by Other Person in One Day.
Divya completes the remaining work alone. So, she completes 8 parts of the work in 14 days. This means that she will complete \(8/14\) parts or \(4/7\) parts of the work in 1 day.
Step 4: Calculate Time taken to do complete work Alone.
In step 1, we decided that Divya + Rakesh do 1 part of work in 1 day. In step 3, we calculated that Divya completes \(4/7\) parts of the work in 1 day. This means that,
Divya + Rakesh = 1 and Divya = \(4/7\)
Rakesh = 1 – 4/7 or 1 – \(4/7\) or \(3/7\) parts.
Rakesh completes \(3/7\) parts of the work in 1 day. The total work is 24 parts. Therefore, he will complete the whole work in \((24*7)/3\) days or 56 days.
Final Answer: 56 Days.
Aniket and Anjali together can complete a work in 22 days. They start together. But, after 7 days, Anjali left the work. If the work is completed after 25 more days, how long will Anjali alone take to do the work?
Deepak and Kunal together can complete a work in 16 days. They start together. But, after 12 days, Kunal left the work. If the work is completed after 20 more days, how long will Kunal alone take to do the work?
John and Alok together can complete a work in 16 days. They start together. But, after 5 days, Alok left the work. If the work is completed after 15 more days, how long will Alok alone take to do the work?
Emma and Sophia together can complete a work in 26 days. They start together. But, after 19 days, Sophia left the work. If the work is completed after 21 more days, how long will Sophia alone take to do the work?
Ramanan and Vivek together can complete a work in 15 days. They start together. But, after 5 days, Vivek left the work. If the work is completed after 13 more days, how long will Vivek alone take to do the work?
Type 12
Question 3: Nikita can do a piece of work in 21 days which Shivani can do in 15 days. Shivani worked at it for 5 days. In how many days can Nikita finish the remaining work?
Step 1: Divide the Total Work in Parts by taking LCM.
LCM of 21 and 15 is 105. This is the total number of parts in which we have divided our work.
Step 2: Calculate Parts of Work Done by Each Group or Person.
Nikita takes 21 days to do the work. So, she will do \(105/21\) parts or 5 parts of the work in 1 day.
Shivani takes 15 days to do the work. So, she will do \(105/15\) parts or 7 parts of the work in 1 day.
Step 3: Calculate Work Left After Given Time.
In 5 days, Shivani will complete 5*7 parts or 35 parts of the work. Work left after 5 days will be 105 – 35 parts or 70 parts.
Step 4: Calculate Time Taken to do the Remaining Work.
Work left is done by Nikita alone. She completes 5 parts of work in 1 day. This means that she will complete the whole work in \(70/5\) days or 14 days.
Final Answer: 14 Days.
Question 4: Akshay can do a piece of work in 28 days which Raghav can do in 42 days. Raghav worked at it for 9 days. In how many days can Akshay finish the remaining work?
Step 1: Divide the Total Work in Parts by taking LCM.
LCM of 28 and 42 is 84. This is the total number of parts in which we have divided our work.
Step 2: Calculate Parts of Work Done by Each Group or Person.
Akshay takes 28 days to complete the work. So, he will do \(84/28\) parts or 3 parts of the work in 1 day.
Raghav takes 42 days to complete the work. So, he will do \(84/42\) parts or 2 parts of the work in 1 day.
Step 3: Calculate Work Left After Given Time.
In 9 days, Raghav will complete 9*2 parts or 18 parts of the work. Work left after 9 days will be 84 – 18 parts or 66 parts.
Step 4: Calculate Time Taken to do the Remaining Work.
Work left is done by Akshay alone. He completes 3 parts of work in 1 day. This means that he will complete the whole work in \(66/3\) days or 22 days.
Final Answer: 22 Days.
Kamalika can do a piece of work in 16 days which Khushi can do in 24 days. Khushi worked at it for 9 days. In how many days can Kamalika finish the remaining work?
Ayushi can do a piece of work in 35 days which Pavitra can do in 25 days. Pavitra worked at it for 10 days. In how many days can Ayushi finish the remaining work?
Krish can do a piece of work in 44 days which Nishita can do in 33 days. Nishita worked at it for 6 days. In how many days can Krish finish the remaining work?
Abhinav can do a piece of work in 39 days which Jacob can do in 26 days. Jacob worked at it for 10 days. In how many days can Abhinav finish the remaining work?
Vaibhav can do a piece of work in 24 days which Avinash can do in 18 days. Avinash worked at it for 9 days. In how many days can Vaibhav finish the remaining work?
Type 13
Question 5: Ajit can do a work in 30 days. When he had worked for 6 days, Sanchit joined him. If they complete the work in 12 more days, in how many days can Sanchit alone finish the work?
Step 1: Divide the Total Work in Parts.
Ajit completes the whole work in 30 days. So, we will assume that the work has 30 parts. This means that he completes 1 part of the work in 1 day.
Step 2: Calculate Work Left After Given Days.
He works alone for 6 days. This means that he completed 6 parts of the work.
Work left to be done now is 30 – 6 parts or 24 parts.
Step 3: Calculate Work Done by Other in One Day.
The remaining work is completed by them together in 12 days. This means that they complete \(24/12\) parts or 2 parts of the work in 1 day. Now, we know that:
Ajit + Sanchit = 2 and Ajit = 1.
Sanchit = 2 – Ajit = 2 – 1 or 1.
So, Sanchit completes 1 part of work in 1 day.
Step 4: Calculate Time taken to do complete work Alone.
The total work is 30 parts and Sanchit completes 1 part of the work in 1 day. This means that he will complete the whole work in \(30/1\) days.
Final Answer: 30 Days.
Question 6: Rishabh can do a work in 24 days. When he had worked for 8 days, Vedant joined him. If they complete the work in 12 more days, in how many days can Vedant alone finish the work?
Step 1: Divide the Total Work in Parts.
Rishabh completes the whole work in 24 days. So, we will assume that the work has 24 parts. This means that he completes 1 part of the work in 1 day.
Step 2: Calculate Work Left After Given Days.
He works alone for 8 days. This means that he completed 8 parts of the work.
Work left to be done now is 24 – 8 parts or 16 parts.
Step 3: Calculate Work Done by Other in One Day.
The remaining work is completed by them together in 12 days. This means that they complete \(16/12\) parts or \(4/3\) parts of the work in 1 day. Now, we know that:
Rishabh + Vedant = \(4/3\) and Rishabh = 1.
Vedant = \(4/3\) – Rishabh = \(4/3\) – 1 or \(1/3\).
So, Vedant completes \(1/3\) part of work in 1 day.
Step 4: Calculate Time taken to do complete work Alone.
The total work is 24 parts and Vedant completes \(1/3\) part of the work in 1 day. This means that he will complete the whole work in \(24*3/1\) days or 72 days.
Final Answer: 72 Days.
Sunil can do a work in 28 days. When he had worked for 7 days, Sunny joined him. If they complete the work in 9 more days, in how many days can Sunny alone finish the work?
Ajit can do a work in 18 days. When he had worked for 6 days, Raghav joined him. If they complete the work in 8 more days, in how many days can Raghav alone finish the work?
Akshay can do a work in 22 days. When he had worked for 7 days, Deepak joined him. If they complete the work in 14 more days, in how many days can Deepak alone finish the work?
Pratik can do a work in 25 days. When he had worked for 7 days, Anirudh joined him. If they complete the work in 9 more days, in how many days can Anirudh alone finish the work?
Angel can do a work in 25 days. When he had worked for 8 days, Jay joined him. If they complete the work in 12 more days, in how many days can Jay alone finish the work?
Type 14
Question 7: Diya and Vidya together can complete a work in 10 days. Vidya alone can complete that work in 35 days. Vidya alone worked for 5 days. After that how long will Diya alone take to complete the work?
Step 1: Divide the Total Work in Parts by taking LCM.
LCM of 10 and 35 is 70. 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.
Diya + Vidya take 10 days to do the work. So, they will do \(70/10\) parts or 7 parts of the work in 1 day.
Vidya takes 35 days to do the work. So, she will do \(70/35\) parts or 2 parts of the work in 1 day.
Diya + Vidya = 7 and Vidya = 2.
Diya = 7 – Vidya = 7 – 2 or 5 parts.
This means that Diya completes 5 parts of the work in 1 day.
Step 3: Calculate Work Left to be Done.
Vidya worked alone for 5 days. Work completed in 5 days is 5*2 parts or 10 parts.
The total work is divided in 70 parts and Vidya completed 10 parts. This means the remaining work is 70 – 10 parts or 60 parts.
Step 4: Calculate Time Taken to do Remaining Work.
Work left to be done now is 60 parts. This means that Diya will complete the remaining work in \(60/5\) days or 12 days.
Final Answer: 12 Days.
Question 8: Anjana and Kritika together can complete a work in 27 days. Kritika alone can complete that work in 45 days. Kritika alone worked for 13 days. After that how long will Anjana alone take to complete the work?
Step 1: Divide the Total Work in Parts by taking LCM.
LCM of 27 and 45 is 135. 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.
Anjana + Kritika take 27 days to do the work. So, they will do \(135/27\) parts or 5 parts of the work in 1 day.
Kritika takes 45 days to do the work. So, she will do \(135/45\) parts or 3 parts of the work in 1 day.
Anjana + Kritika = 5 and Kritika = 3.
Anjana = 5 – Kritika = 5 – 3 or 2 parts.
This means that Anjana completes 2 parts of the work in 1 day.
Step 3: Calculate Work Left to be Done.
Kritika worked alone for 13 days. Work completed in 13 days is 13*3 parts or 39 parts.
The total work is divided in 135 parts and Vidya completed 39 parts. This means the remaining work is 135 – 39 parts or 96 parts.
Step 4: Calculate Time Taken to do Remaining Work.
Work left to be done now is 96 parts. This means that Anjana will complete the remaining work in \(96/2\) days or 48 days.
Final Answer: 48 Days.
Anil and Simran together can complete a work in 19 days. Simran alone can complete that work in 30 days. Simran alone worked for 8 days. After that how long will Anil alone take to complete the work?
Aswini and Gayatri together can complete a work in 27 days. Gayatri alone can complete that work in 42 days. Gayatri alone worked for 12 days. After that how long will Aswini alone take to complete the work?
Neeraj and Priyanka together can complete a work in 18 days. Priyanka alone can complete that work in 21 days. Priyanka alone worked for 10 days. After that how long will Neeraj alone take to complete the work?
Neha and Priyanka together can complete a work in 16 days. Priyanka alone can complete that work in 32 days. Priyanka alone worked for 11 days. After that how long will Neha alone take to complete the work?
Manu and Avinash together can complete a work in 20 days. Avinash alone can complete that work in 24 days. Avinash alone worked for 6 days. After that how long will Manu alone take to complete the work?
Type 15
Question 9: Avinash can do a piece of work in 16 days. When he had worked for 3 days, Rajeev joined him. If complete work was finished in 12 days, Rajeev can alone finish that work in.
Step 1: Divide the Total Work in Parts.
Avinash completes the whole work together in 16 days. So, we will assume that the work has 16 parts. This means that Avinash completes 1 part of work each day.
Step 2: Calculate Work Left After Given Days.
He works for 3 days. This means that he completed 3 parts of the work.
Work left to be done now is 16 – 3 parts or 13 parts.
Step 3: Calculate Work Done by them Together in One Day.
The total time taken to complete the work is 12 days. Avinash worked alone for first 3 days. This means that they worked together for 12 – 3 days or 9 days.
So, they can complete \(13/9\) parts of work in one day when working together.
Step 4: Calculate Time taken by Given Person.
In step 1, we assumed that Avinash completes 1 part of work in 1 day. This means that,
Avinash + Rajeev = \(13/9\) and Avinash = 1.
Rajeev = \(13/9\) – Avinash = \(13/9\) – 1 or \(4/9\).
This means that Rajeev completes \(4/9\) parts of work in 1 day.
Total work has 16 parts. So, Rajeev will take \((16*9)/4\) days or 36 days to complete the whole work.
Final Answer: 36 Days.
Question 10: John can do a piece of work in 49 days. When he had worked for 9 days, Andrew joined him. If complete work was finished in 39 days, Andrew can alone finish that work in.
Step 1: Divide the Total Work in Parts.
John completes the whole work together in 49 days. So, we will assume that the work has 49 parts. This means that Avinash completes 1 part of work each day.
Step 2: Calculate Work Left After Given Days.
He works for 9 days. This means that he completed 9 parts of the work.
Work left to be done now is 49 – 9 parts or 40 parts.
Step 3: Calculate Work Done by them Together in One Day.
The total time taken to complete the work is 39 days. John worked alone for first 9 days. This means that they worked together for 39 – 9 days or 30 days.
So, they can complete \(40/30\) parts or \(4/3\) parts of work in one day when working together.
Step 4: Calculate Time taken by Given Person.
In step 1, we assumed that John completes 1 part of work in 1 day. This means that,
John + Andrew = \(4/3\) and John = 1.
Andrew = \(4/3\) – John = \(4/3\) – 1 or \(1/3\).
This means that Andrew completes \(1/3\) parts of work in 1 day.
Total work has 49 parts. So, Andrew will take \((49*3)/1\) days or 147 days to complete the whole work.
Final Answer: 147 Days.
Ankit can do a piece of work in 15 days. When he had worked for 3 days, Rahul joined him. If complete work was finished in 12 days, Rahul can alone finish that work in.
Sadaf can do a piece of work in 46 days. When he had worked for 10 days, William joined him. If complete work was finished in 28 days, William can alone finish that work in.
Rishabh can do a piece of work in 35 days. When he had worked for 7 days, Aryan joined him. If complete work was finished in 15 days, Aryan can alone finish that work in.
Arun can do a piece of work in 15 days. When he had worked for 3 days, Ramanan joined him. If complete work was finished in 11 days, Ramanan can alone finish that work in.
Lily can do a piece of work in 19 days. When he had worked for 3 days, Sanchit joined him. If complete work was finished in 15 days, Sanchit can alone finish that work in.