Time & Work - Solved Problem

Time & Work - Solved Problem - 1

Question 1
Prakash can complete a piece of work in 24 days and Praveen can complete the same piece of work in 36 days. If Prakash and Praveen work together, how long would they take to complete the work?
a) 14.4 days 
b) 15.5 days 
c) 12 days 
d) 20 days
Answer : a) 14.4 days
Solution :
Prakash can complete in one day = 1/24 of work.
Praveen can complete in one day = 1/36 of work.
Prakash and Praveen can complete in one day = 1/24 + 1/36 of work.
= 3 + 2 / 72
= 5/72
Both can complete the work in 72/5 days.i.e., 14.4 days

Question 2
Bala and Aruna can complete a work in 30 days. Bala can do it alone in 50 days. How many days would Aruna take to complete the work alone?
a) 100 days b) 120 days c) 90 days d) 75 days
Answer : d) 75 days
Solution :
By using the alternate method as mentioned in Question 1, we are going to solve further problems.
LCM of 30 and 50 is 150.
Bala and Aruna can complete whole work in 30 days. In 1 day they can complete 5(150/30) of the work.
Bala alone can can complete whole work in 50 days. In 1 day he can complete 3(150/30) of the work.
Aruna alone can complete in 1 day (5 - 3)of the work.
Therefore, Aruna will complete the whole work in 150/2 = 75 days.

Question 3
P can wash some number of clothes in 6 hours and Q can wash same in 18 hours. After 4 hours, P leaves from his job. Then how long must Q work to
wash the remaining clothes?
a) 6 hours b) 12 hours c) 8 hours d) 4 hours
Answer : a) 6 hours
Solution :
The L.C.M of 6, 18, and 4 is 36. so assume that the total number of clothes is 36.
36 clothes can be washed by P in 6 hours.Hence P’s speed is 6 =(36/6) clothes per hour.
Before P's absent, he would have washed 6x4 i.e. 24 clothes.
The remaining is 12 clothes, which will be done by Q in 6 = (18/36 x 12) hours. (as it is indicated that the entire job can be finished by Q in 18 hours)
Hence the answer is 6 hours.

Question 4
Vanitha can type a file in 10 hours. Her friend joins after 3 hours.Together they type for 4 hours to complete the file. How many hours would her friend take to type the file alone?
a) 13 1/3 hours b) 12 1/5 hours c) 11 1/2 hours d) 10 1/7 hours
Answer : a) 13 1/3 hours.
Solution :
In some cases, instead of L.C.M you can take multiples of L.C.M or simply multiply the number involved in the problem.
In this problem, the numbers involved are 10, 3 and 4.
Multiplying all of them, we get 120 which is the number of files to be typed.
Vanitha can type 120 files in 10 hours, so in 1 hour 12 files.
She works alone for 3 hours to produce 3x12 files before a helper joins.
Together they finish the balance requirement of 120-36 = 84 in 4 hours, so in 1 hour 21(84/4) files are completed.
But out of this 21, Vanitha is producing 12 files per hour.
Therefore, her friend must be producing 9 files per hour.
If her friend alone types 120 files, then she will complete in 120/9 hours i.e.,13 1/3 hours

Question 5
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 6
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 7
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 8
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.