Dear Reader,
Below are four problems based on the concept of time and work for your practice.
Note:
Work from Days:
If A can do a piece of work in n days, then A's 1 day's work = 1/n.
Days from Work:
If A's 1 day's work = 1/n, then A can finish the work in n days.
Question 1
Vidhya can complete a piece of work in 30 days and Nithya in 40 days. Find the remaining work left to complete, if they work together for 8 days.
a) 2/5 b) 1/12 c) 8/15 d) 4/19
Answer : c) 8/15
Solution :
Vidhya's 1 day work = 1/30
Nithya's 1 day work = 1/40
Then, (Vidhya + Nithya)'s 1 day work = 1/30 + 1/40 = 7/120
And (Vidhya + Nithya)'s 8 day's work = 8 x(7/120) = 7/15
Therefore, Remaining work = (1 - 7/15) = 8/15
Question 2
P and Q separately can dig a well in 32 days and 24 days respectively. They completed the same work in 8 days with the help of R. Then R can dig a well alone in:
a) 18 2/5 days b) 19 1/5 days c) 12 3/5 days d) 17 4/5 days
Answer : b)19 1/5 days
Solution :
(P + Q + R)'s 1 day work = 1/8,
P's 1 day work = 1/32,
Q's 1 day work = 1/24.
Therefore R's 1 day work = 1/8 - (1/32 + 1/24) = (1/8 - 7/96)= 5/96
So, R alone can do the work in 96/5 days = 19 1/5 days.
Hence the required answer is 19 1/5 days.
Question 3
A man A can do a piece of work in 8 days, man B can do the same piece of work in 10 days while man C can do it in 12 days. They started work together but after 2 days A left the work and the remaining work has been completed by B and C. Find when will the work be completed (Approximately).
a) 4 days b) 2 days c) 3 days d) 5 days.
Answer : a) 4 days.
Solution :
(A + B + C)'s 1 day work = (1/8 + 1/10 + 1/12) = (15 + 12 + 10)/120 = 37/120
Work done by A, B and C in 2 days = (37/120) x 2 = 37/60
Remaining work = 1- 37/60 = 23/60
(B + C)'s 1 day work = (1/10 + 1/12) = 11/60
Now, 11/60 work is done by B and C in 1 day.
So, 23/60 work will be done by B and C in (60/11 x 23/60) = 23/11 days = 2 days(approximately)
So, the work will be finished approximately 2 days after A had left.i.e., around 4 days.
Hence the answer is 4 days.
Question 4
Chandru can complete a work in 36 days and Pavithra can complete the same work in 30 days. If Pavithra worked for 20 days and left the work, in how many days, Chandru alone can complete the remaining job?
a) 12 days b) 11 days c) 18 days d) 10 days
Answer : a) 12 days.
Solution :
Pavithra's 1 day work = 1/30
Pavithra's 20 day's work = 1/30 x 20 = 2/3
Remaining work = 1 - 2/3 = 1/3
Now, Chandru's 1 day work = 1/36
Therefore, 1/3 work is done by him in 36 x 1/3 = 12 days.
Below are four problems based on the concept of time and work for your practice.
Note:
Work from Days:
If A can do a piece of work in n days, then A's 1 day's work = 1/n.
Days from Work:
If A's 1 day's work = 1/n, then A can finish the work in n days.
Question 1
Vidhya can complete a piece of work in 30 days and Nithya in 40 days. Find the remaining work left to complete, if they work together for 8 days.
a) 2/5 b) 1/12 c) 8/15 d) 4/19
Answer : c) 8/15
Solution :
Vidhya's 1 day work = 1/30
Nithya's 1 day work = 1/40
Then, (Vidhya + Nithya)'s 1 day work = 1/30 + 1/40 = 7/120
And (Vidhya + Nithya)'s 8 day's work = 8 x(7/120) = 7/15
Therefore, Remaining work = (1 - 7/15) = 8/15
Question 2
P and Q separately can dig a well in 32 days and 24 days respectively. They completed the same work in 8 days with the help of R. Then R can dig a well alone in:
a) 18 2/5 days b) 19 1/5 days c) 12 3/5 days d) 17 4/5 days
Answer : b)19 1/5 days
Solution :
(P + Q + R)'s 1 day work = 1/8,
P's 1 day work = 1/32,
Q's 1 day work = 1/24.
Therefore R's 1 day work = 1/8 - (1/32 + 1/24) = (1/8 - 7/96)= 5/96
So, R alone can do the work in 96/5 days = 19 1/5 days.
Hence the required answer is 19 1/5 days.
Question 3
A man A can do a piece of work in 8 days, man B can do the same piece of work in 10 days while man C can do it in 12 days. They started work together but after 2 days A left the work and the remaining work has been completed by B and C. Find when will the work be completed (Approximately).
a) 4 days b) 2 days c) 3 days d) 5 days.
Answer : a) 4 days.
Solution :
(A + B + C)'s 1 day work = (1/8 + 1/10 + 1/12) = (15 + 12 + 10)/120 = 37/120
Work done by A, B and C in 2 days = (37/120) x 2 = 37/60
Remaining work = 1- 37/60 = 23/60
(B + C)'s 1 day work = (1/10 + 1/12) = 11/60
Now, 11/60 work is done by B and C in 1 day.
So, 23/60 work will be done by B and C in (60/11 x 23/60) = 23/11 days = 2 days(approximately)
So, the work will be finished approximately 2 days after A had left.i.e., around 4 days.
Hence the answer is 4 days.
Question 4
Chandru can complete a work in 36 days and Pavithra can complete the same work in 30 days. If Pavithra worked for 20 days and left the work, in how many days, Chandru alone can complete the remaining job?
a) 12 days b) 11 days c) 18 days d) 10 days
Answer : a) 12 days.
Solution :
Pavithra's 1 day work = 1/30
Pavithra's 20 day's work = 1/30 x 20 = 2/3
Remaining work = 1 - 2/3 = 1/3
Now, Chandru's 1 day work = 1/36
Therefore, 1/3 work is done by him in 36 x 1/3 = 12 days.
