Examples and Practice Question (16 to 20)
Type 16
Question 1: Work done by Anirudh in 2 days is equal to work done by Mayank in 8 days. If Anirudh can complete a work in 45 days, how long will they take to complete it together?
Step 1: Divide the Total Work in Parts.
Anirudh can complete the whole work in 45 days. So, we will assume that the work has 45 parts. This means that he completed 1 part of the work in 1 day.
Step 2: Calculate the Ratio of Efficiency.
Work done by Anirudh in 2 days is equal to work done by Mayank in 8 days. So,
8*Mayank = 2*Aditya
Mayank = \(Aditya/4\)
Mayank is 4 times less efficient than Anirudh. Also, Anirudh completes 1 part of work in 1 day. This means that Mayank completes \(1/4\) parts of the work in 1 day.
Step 3: Calculate Work Done by Them in One Day.
Mayank and Anirudh will complete \(1/4\) + 1 parts or \(5/4\) parts of work together in 1 day.
Step 4: Calculate Time taken to do complete Work.
The total work is divided in 45 parts. The complete \(5/4\) parts of work in 1 day. This means that the whole work will be completed in \((45*4)/5\) days or 36 days.
Final Answer: 36 Days.
Question 2: Work done by Lily in 10 days is equal to work done by Aditya in 4 days. If Lily can complete a work in 42 days, how long will they take to complete it together?
Step 1: Divide the Total Work in Parts.
Lily can complete the whole work in 42 days. So, we will assume that the work has 42 parts. This means that she completed 1 part of the work in 1 day.
Step 2: Calculate the Ratio of Efficiency.
Work done by Lily in 10 days is equal to work done by Aditya in 4 days. So,
4*Aditya = 10*Lily
Aditya = \((10*Lily)/4\) or \((5*Lily)/2\)
Aditya is \(5/2\) times more efficient than Lily. Also, Lily completes 1 part of work in 1 day. This means that Aditya completes \(5/2\) parts of the work in 1 day.
Step 3: Calculate Work Done by Them in One Day.
Aditya and Lily will complete \(5/2\) + 1 parts or \(7/2\) parts of work together in 1 day.
Step 4: Calculate Time taken to do complete Work.
The total work is divided in 42 parts. The complete \(7/2\) parts of work in 1 day. This means that the whole work will be completed in \((42*2)/7\) days or 12 days.
Final Answer: 12 Days.
Work done by Anamika in 4 days is equal to work done by Harish in 5 days. If Anamika can complete a work in 36 days, how long will they take to complete it together?
Work done by Ananya in 6 days is equal to work done by Anurag in 5 days. If Ananya can complete a work in 33 days, how long will they take to complete it together?
Work done by Vaibhav in 6 days is equal to work done by Sam in 10 days. If Vaibhav can complete a work in 40 days, how long will they take to complete it together?
Work done by Pranav in 4 days is equal to work done by Tanvi in 7 days. If Pranav can complete a work in 44 days, how long will they take to complete it together?
Work done by Anushri in 3 days is equal to work done by Neha in 5 days. If Anushri can complete a work in 32 days, how long will they take to complete it together?
Type 17
Question 3: Dhruv and Rakesh are working together on an assignment. Dhruv takes 15 hours to type 20 pages on a computer, while Rakesh takes 6 hours to type 16 pages. How much time will they take working together on two different computers to type an assignment of 152 pages?
Step 1: Calculate Total Pages Typed Per Hour.
Dhruv types \(20/15\) pages or \(4/3\) pages per hour. Rakesh types \(16/6\) pages or \(8/3\) pages per hour.
Together, they will type \(4/3\) + \(8/3\) pages = \(12/3\) pages or 4 pages per hour.
Step 2: Calculate Time Taken to Type all Pages.
They have to type 152 pages. If they type 4 pages per hour, it will take them \(152/4\) hours or 38 hours to type everything.
Final Answer: 38 Hours.
Question 4: Emily and Tisha are working together on an assignment. Emily takes 12 hours to type 48 pages on a computer, while Tisha takes 7 hours to type 42 pages. How much time will they take working together on two different computers to type an assignment of 130 pages?
Step 1: Calculate Total Pages Typed Per Hour.
Emily types \(48/12\) pages or 4 pages per hour. Tisha types \(42/7\) pages or 6 pages per hour.
Together, they will type 4 + 6 pages = 10 pages per hour.
Step 2: Calculate Time Taken to Type all Pages.
They have to type 130 pages. If they type 10 pages per hour, it will take them \(130/10\) hours or 13 hours to type everything.
Final Answer: 13 Hours.
Rajeev and Indhumati are working together on an assignment. Rajeev takes 8 hours to type 48 pages on a computer, while Indhumati takes 8 hours to type 40 pages. How much time will they take working together on two different computers to type an assignment of 176 pages?
Mahima and Sneha are working together on an assignment. Mahima takes 6 hours to type 28 pages on a computer, while Sneha takes 12 hours to type 40 pages. How much time will they take working together on two different computers to type an assignment of 160 pages?
Harish and Parth are working together on an assignment. Harish takes 5 hours to type 40 pages on a computer, while Parth takes 15 hours to type 45 pages. How much time will they take working together on two different computers to type an assignment of 110 pages?
Prince and Vinay are working together on an assignment. Prince takes 12 hours to type 24 pages on a computer, while Vinay takes 10 hours to type 28 pages. How much time will they take working together on two different computers to type an assignment of 120 pages?
Ishita and Arti are working together on an assignment. Ishita takes 12 hours to type 48 pages on a computer, while Arti takes 11 hours to type 33 pages. How much time will they take working together on two different computers to type an assignment of 119 pages?
Type 18
Question 5: Aditya does \(3/5\) of a piece of work in 30 days. He then calls in Anish and they finish the remaining work in 12 days. How long Anish alone will take to do whole work alone?
Step 1: Divide the Total Work in Parts.
Aditya completes \(3/5\) part of the work in 30 days. This means that he will complete the whole work alone in \((30*5)/3\) days or 50 days. We will assume the work has 50 parts. So, he completes 1 part of the work in 1 day.
Step 2: Calculate Work Done Together in 1 day.
Aditya completed \((50*3)/5\) parts or 30 parts of the work alone. Remaining work is 50 – 30 parts or 20 parts.
They complete the remaining work in 12 days. This means that they completed \(20/12\) parts or \(5/3\) parts of the work in 1 day.
Step 3: Calculate the Work Done by Given Person Alone.
Aditya and Anish complete \(5/3\) parts of the work in 1 day. Aditya alone completes 1 part of the work in 1 day. This means that Anish alone will complete \(5/3\) – 1 parts or \(2/3\) parts of the work in 1 day.
Step 4: Calculate Time taken to do complete work Alone.
The total work is 50 parts and Anish completes \(2/3\) parts of the work in 1 day. This means that he will complete the whole work alone in \((50*3)/2\) days or 75 days.
Final Answer: 75 Days.
Question 6: Krish does \(8/13\) of a piece of work in 40 days. He then calls in Sam and they finish the remaining work in 12 days. How long Sam alone will take to do whole work alone?
Step 1: Divide the Total Work in Parts.
Krish completes \(8/13\) part of the work in 40 days. This means that he will complete the whole work alone in \((40*13)/8\) days or 65 days. We will assume the work has 65 parts. So, he completes 1 part of the work in 1 day.
Step 2: Calculate Work Done Together in 1 day.
Krish completed \((65*8)/13\) parts or 40 parts of the work alone. Remaining work is 65 – 40 parts or 25 parts.
They complete the remaining work in 12 days. This means that they completed \(25/12\) parts of the work in 1 day.
Step 3: Calculate the Work Done by Given Person Alone.
Krish and Sam complete \(25/12\) parts of the work in 1 day. Krish alone completes 1 part of the work in 1 day. This means that Sam alone will complete \(25/12\) – 1 parts or \(13/12\) parts of the work in 1 day.
Step 4: Calculate Time taken to do complete work Alone.
The total work is 65 parts and Sam completes \(13/12\) parts of the work in 1 day. This means that he will complete the whole work alone in \((65*12)/13\) days or 60 days.
Final Answer: 60 Days.
Manish does \(1/4\) of a piece of work in 35 days. He then calls in Rakesh and they finish the remaining work in 7 days. How long Rakesh alone will take to do whole work alone?
Ajay does \(2/3\) of a piece of work in 27 days. He then calls in Kunal and they finish the remaining work in 9 days. How long Kunal alone will take to do whole work alone?
Rakesh does \(1/2\) of a piece of work in 26 days. He then calls in Varun and they finish the remaining work in 13 days. How long Varun alone will take to do whole work alone?
Naveen does \(4/7\) of a piece of work in 20 days. He then calls in James and they finish the remaining work in 8 days. How long James alone will take to do whole work alone?
Shivam does \(9/14\) of a piece of work in 26 days. He then calls in Tushar and they finish the remaining work in 10 days. How long Tushar alone will take to do whole work alone?
Type 19
Question 7: Prateek can do \(3/7\) of a work in 24 days. Aryan can do \(5/7\) of the work in 30 days. In how many days can both Prateek and Aryan together do the work?
Step 1: Calculate Time Taken by Each Person for Complete Work.
Prateek completes \(3/7\) part of the work in 24 days. So, he will take \((24*7)/3\) days or 56 days to complete the whole work.
Aryan completes \(5/7\) part of the work in 30 days. So, he will take \((30*7)/5\) days or 42 days to complete the whole work.
Step 2: Divide the Total Work in Parts by taking LCM.
LCM of 56 and 42 will be 168. This is the total number of parts in which we have divided our work.
Step 3: Calculate Work Done per Day.
Prateek takes 56 days to complete the whole work. This means that he will complete \(168/56\) parts or 3 parts of work in 1 day.
Aryan takes 42 days to complete the whole work. This means that he will complete \(168/42\) parts or 4 parts of work in 1 day.
Together, they will complete 3 + 4 parts or 7 parts of work in 1 day.
Step 4: Calculate Time Taken to do Remaining Work.
Total work to be done is 168 parts. This means that they will complete the whole work in \(168/7\) days or 24 days.
Final Answer: 24 Days.
Question 8: Anusha can do \(4/7\) of a work in 48 days. Pawan can do \(2/3\) of the work in 28 days. In how many days can both Anusha and Pawan together do the work?
Step 1: Calculate Time Taken by Each Person for Complete Work.
Anusha completes \(4/7\) part of the work in 48 days. So, he will take \((48*7)/4\) days or 84 days to complete the whole work.
Aryan completes \(2/3\) part of the work in 28 days. So, he will take \((28*3)/2\) days or 42 days to complete the whole work.
Step 2: Divide the Total Work in Parts by taking LCM.
LCM of 84 and 42 will be 84. This is the total number of parts in which we have divided our work.
Step 3: Calculate Work Done per Day.
Anusha takes 84 days to complete the whole work. This means that she will complete \(84/84\) part or 1 part of work in 1 day.
Pawan takes 42 days to complete the whole work. This means that he will complete \(84/42\) parts or 2 parts of work in 1 day.
Together, they will complete 1 + 2 parts or 3 parts of work in 1 day.
Step 4: Calculate Time Taken to do Remaining Work.
Total work to be done is 84 parts. This means that they will complete the whole work in \(84/3\) days or 28 days.
Final Answer: 28 Days.
Ananya can do \(1/7\) of a work in 16 days. Pranav can do \(1/3\) of the work in 28 days. In how many days can both Ananya and Pranav together do the work?
Abhishek can do \(1/6\) of a work in 28 days. Diksha can do \(3/7\) of the work in 40 days. In how many days can both Abhishek and Diksha together do the work?
Sanjay can do \(2/5\) of a work in 24 days. Arushi can do \(1/2\) of the work in 45 days. In how many days can both Sanjay and Arushi together do the work?
Rohan can do \(1/3\) of a work in 49 days. Rhea can do \(4/9\) of the work in 49 days. In how many days can both Rohan and Rhea together do the work?
Deepak can do \(4/5\) of a work in 48 days. Shashank can do \(4/5\) of the work in 24 days. In how many days can both Deepak and Shashank together do the work?
Type 20
Question 9: Kavya can do a piece of work in 45 days which Andrew can do in 25 days. Andrew worked at it for 5 days. In how many days can Kavya finish the remaining work?
Step 1: Divide the Total Work in Parts.
LCM of 45 and 25 will be 225. This is the total number of parts in which we have divided our work.
Step 2: Calculate Work Done by Each Person.
Kavya takes 45 days to complete the whole work. This means that she will complete \(225/45\) parts or 5 parts of work in 1 day.
Andrew takes 25 days to complete the whole work. This means that he will complete \(225/25\) parts or 9 parts of work in 1 day.
Step 3: Calculate Work Left to be Done.
Andrew worked alone for 5 days. So, he completed 5*9 parts or 45 parts of the work.
Total work is 225 parts. So, work left to be done is 225 – 45 parts or 180 parts.
Step 4: Calculate Time taken to do Remaining Work.
Kavya has to do 180 parts of work alone. She completes 5 parts of work in 1 day. This means that she will take \(180/5\) days or 36 days to complete the whole work.
Final Answer: 36 Days.
Question 10: Ajit can do a piece of work in 45 days which Raghav can do in 21 days. Raghav worked at it for 7 days. In how many days can Ajit finish the remaining work?
Step 1: Divide the Total Work in Parts.
LCM of 45 and 21 will be 315. This is the total number of parts in which we have divided our work.
Step 2: Calculate Work Done by Each Person.
Ajit takes 45 days to complete the whole work. This means that he will complete \(315/45\) parts or 7 parts of work in 1 day.
Raghav takes 21 days to complete the whole work. This means that he will complete \(315/21\) parts or 15 parts of work in 1 day.
Step 3: Calculate Work Left to be Done.
Raghav worked alone for 7 days. So, he completed 7*15 parts or 105 parts of the work.
Total work is 315 parts. So, work left to be done is 315 – 105 parts or 210 parts.
Step 4: Calculate Time taken to do Remaining Work.
Ajit has to do 210 parts of work alone. He completes 7 parts of work in 1 day. This means that he will take \(210/7\) days or 30 days to complete the whole work.
Final Answer: 30 Days.
Tisha can do a piece of work in 24 days which Anthony can do in 18 days. Anthony worked at it for 6 days. In how many days can Tisha finish the remaining work?
Anushri can do a piece of work in 19 days which Vidya can do in 38 days. Vidya worked at it for 12 days. In how many days can Anushri finish the remaining work?
Abdul can do a piece of work in 42 days which Joshua can do in 30 days. Joshua worked at it for 10 days. In how many days can Abdul finish the remaining work?
Rhea can do a piece of work in 40 days which Daniel can do in 15 days. Daniel worked at it for 6 days. In how many days can Rhea finish the remaining work?
Ananya can do a piece of work in 21 days which Anish can do in 42 days. Anish worked at it for 6 days. In how many days can Ananya finish the remaining work?