Time & Work is a favourite area considering placement test of any big company like Wipro. You can always expect few questions from time and work section. Though tagged as wipro sample paper, one can expect these kinds of questions in other papers as well.
Question 1
Consider three people A,B and C. Let A and B can finish a job in 21 days, B and C in 14 days and A and C in 28 days. Who will take the least time when working independently ?
Options : 1) A 2) B 3) C 4) Can't be determined
Answer 1
Correct answer is B
Consider WA, WB and WC be the work done per day by A,B and C respectively. Then
WA + WB = 1/21 -- eq 1
WB + WC = 1/14 -- eq 2
WA + WC = 1/28 -- eq 3
Eq 2 - Eq 3 will give
WB - WA = 1/14 - 1/28 = 1/28 -- eq 4
Eq 1 + Eq 4 will give
2WB = 1/21 + 1/28 = 7/84
WB = 7/168
Sub value of WB in eq 1, we get
WA = 1/21 - 7/168 = 1/168.
Sub value of WA in eq 3, we get
wc = 1/28 - WA = 1/28 - 1/168 = 5/168
Since WB (work done by B per day) is greater when compared to WA and WB clearly B will be able to the maximum work on any given day and hence he should consume least amount of time when working independently.
Question 2
Consider two postmen A and B respectively. A is young and can deliver 20 parcels in 3 hours while B is older than A and can deliver only 15 parcels in 4 hours. If the total number of parcels to deliver is 60, how long they will take working together.
a. 121/12 hours b. 144/36 hours c. 144/25 hours d. 121/25 hours
Answer 2
Correct ans is option c. 144/25 hours.
A can deliver 20 parcels in 3 hours. Hence for 1 hour he can deliver 20/3 parcels.
B can deliver 15 parcel in 4 hours. Hence for 1 hour B needs 15/4 parcels.
When A and B work together, for 1 hour they can deliver, 20/3 + 15/4 parcles = 80 + 45 /12 = 125/12 parcels.
Hence to deliver 60 parcels they would require : 60 X 12/125 = 720/125 = 144/25 hours
Question 3
Consider a courier company A which can deliver 100 parcels in 5 days with 5 men working for 8 hours a day. Consider another courier company B where every employee is equally effecient as that of company B. Company B is short of one man when compared to A and has a policy of asking its workers to work only for 6 hours a day. How long (in days) company B will take to deliver 100 parcels.
Options : a. 8.3 b. 24 c. 12 d 6.6
Answer
Correct answer is a. 8.3 days
Total amount of work W = N x D X W
where N = number of men, D = number of days, W = amount of work per day
Applying the above formula for company A we get,
Work done by company A to deliver 100 parcels = 5 X 5 X 8 = 200 -- eq 1
Work done by company B to deliver 100 parcels = 4 X D x 6 = 24D -- eq 2
Since the work to be done is same in both the cases, eq 1 = eq2
or 200 = 24D or D = 8.3
Question 1
Consider three people A,B and C. Let A and B can finish a job in 21 days, B and C in 14 days and A and C in 28 days. Who will take the least time when working independently ?
Options : 1) A 2) B 3) C 4) Can't be determined
Answer 1
Correct answer is B
Consider WA, WB and WC be the work done per day by A,B and C respectively. Then
WA + WB = 1/21 -- eq 1
WB + WC = 1/14 -- eq 2
WA + WC = 1/28 -- eq 3
Eq 2 - Eq 3 will give
WB - WA = 1/14 - 1/28 = 1/28 -- eq 4
Eq 1 + Eq 4 will give
2WB = 1/21 + 1/28 = 7/84
WB = 7/168
Sub value of WB in eq 1, we get
WA = 1/21 - 7/168 = 1/168.
Sub value of WA in eq 3, we get
wc = 1/28 - WA = 1/28 - 1/168 = 5/168
Since WB (work done by B per day) is greater when compared to WA and WB clearly B will be able to the maximum work on any given day and hence he should consume least amount of time when working independently.
Question 2
Consider two postmen A and B respectively. A is young and can deliver 20 parcels in 3 hours while B is older than A and can deliver only 15 parcels in 4 hours. If the total number of parcels to deliver is 60, how long they will take working together.
a. 121/12 hours b. 144/36 hours c. 144/25 hours d. 121/25 hours
Answer 2
Correct ans is option c. 144/25 hours.
A can deliver 20 parcels in 3 hours. Hence for 1 hour he can deliver 20/3 parcels.
B can deliver 15 parcel in 4 hours. Hence for 1 hour B needs 15/4 parcels.
When A and B work together, for 1 hour they can deliver, 20/3 + 15/4 parcles = 80 + 45 /12 = 125/12 parcels.
Hence to deliver 60 parcels they would require : 60 X 12/125 = 720/125 = 144/25 hours
Question 3
Consider a courier company A which can deliver 100 parcels in 5 days with 5 men working for 8 hours a day. Consider another courier company B where every employee is equally effecient as that of company B. Company B is short of one man when compared to A and has a policy of asking its workers to work only for 6 hours a day. How long (in days) company B will take to deliver 100 parcels.
Options : a. 8.3 b. 24 c. 12 d 6.6
Answer
Correct answer is a. 8.3 days
Total amount of work W = N x D X W
where N = number of men, D = number of days, W = amount of work per day
Applying the above formula for company A we get,
Work done by company A to deliver 100 parcels = 5 X 5 X 8 = 200 -- eq 1
Work done by company B to deliver 100 parcels = 4 X D x 6 = 24D -- eq 2
Since the work to be done is same in both the cases, eq 1 = eq2
or 200 = 24D or D = 8.3
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