Time and Work Test

Result

Time and Work Test - 5

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Question 1
1 / -0

A pit can be dug by 4 men in 16 days. How many days will 8 men take for the same work?

A
6 days

B
8 days

C
7 days

D
5 days

E
None of these

Solution

A pit can be dug by 4 men in 16 days.
Therefore, a pit can be dug by 1 man in 64 days.
Each man does 1/64 of the work in 1 day.
Now, work done by 8 men in one day = 8/64 = 1/8
Thus, 8 men can do the work in 8 days.
Question 2
1 / -0

An inlet pipe fills a cistern in 3 hours. However, due to leakage at the bottom, it takes half an hour longer. When the cistern is full, how long would the leak take to empty the cistern?

A
28 hours

B
27 hours

C
29 hours

D
32 hours

E
None of these

Solution

Inlet fills the cistern in 3 hours.
Due to the leakage, it takes 4 hours to fill it.
Now, according to the question,
Time taken by the leak to empty the cistern = = = 28 hours
Question 3
1 / -0

A contractor undertakes a certain work to be completed in 55 days and employs 48 men to do it. In 11 days, only 1/6^th of the work has been done. How many extra men should he employ in order to complete the work in the allotted time?

A
8

B
12

C
16

D
18

E
None of these

Solution

Let work done by 1 man in 1 day = m
Let total amount of work = 6W
As in 11 days, only 1/6^th of the work is done, we have 48 × m × 11 = W
Or m = W/(11 × 48) ... (i)
Let n men be employed to complete the rest of the work (6W - W = 5W) in 44 (55 - 11 = 44) days.
So, n × m × 44 = 5W ... (ii)
Putting the value of m from equation (i) into equation (ii) and solving for n, we get n = 60
Thus, number of more men to be employed = 60 - 48 = 12
Hence, answer option 2 is correct.
Question 4
1 / -0

How many patients does the doctor examine in a day if he examines 5 patients in 3 hours with breaks of 10 minutes between two consecutive patients and he works for 10 hours and 15 minutes per day?

A
16

B
15

C
17

D
18

E
None of these

Solution

3 hours = 3 x 60 minutes = 180 minutes
In 180 minutes he examines 5 patients with 4 breaks of 10 minutes each between 2 consecutive patients.
Thus, time taken for examining 1 patient = ((180 - 40)/5) minutes = 28 minutes
10 hours 15 minutes = (10 x 60 + 15 = 615) minutes
If he examines n patients in a day, then he has (n - 1) break periods of 10 minutes
So, 28n + 10(n - 1) = 615.
Or, n = 16.447
But, the number of patients has to be integral.
So, n = 16 or 17
Time taken to examine 16 patients = (28 x 16 + 10 x 15) minutes = 598 minutes
Thus, after examining 16 patients, he is left with (615 - 598 = 17) minutes.
As he needs 28 minute to examine 1 patient, he cannot examine another patient after having examined 16 patients.
Hence, he examines 16 patients.
Thus, answer option 1 is correct
Question 5
1 / -0

A alone can do a piece of work in 6 days and B alone can do it in 8 days. How many days will it take both A and B together to finish twice the same work?

A
7/24

B
48/7

C
7/12

D
12/7

E
7/48

Solution

A can do 1/6 of the work in one day and B can do 1/8 of the work in one day.
Together, they can do 1/6 + 1/8 = 7/24 work in one day.
Therefore, together they can complete the work in 24/7 days.
Hence, the total number of days it will take them to complete twice the same work = 48/7.
Question 6
1 / -0

If 10 men can clean 2 acres of lawn in 12 days, then how many men can clean 3 acres of lawn in 6 days?

A
30 men

B
32 men

C
31 men

D
24 men

E
None of these

Solution

Apply the formula,(10 ×12)/2 = (M₂ × 6)/3
M₂ = 30
Question 7
1 / -0

A group of 4 men can dig a pit in 15 days. If a man works half as much more as a boy, then 8 men and 6 boys can dig it in

A
6 days

B
10 days

C
7 days

D
5 days

E
None of these

Solution

One man = 1.5 boys
6 boys = 4 men
12 men (8 men + 6 boys = 12 men) can complete the work in 15 4/12 = 5 days.
Question 8
1 / -0

When sugar is 10 kg for Rs. 100, a sum of money maintains a family of 18 men for 15 days. How long will the same amount of money maintain a family of 6 men when sugar is 14 kg for Rs. 100?

A
57 days

B
63 days

C
67 days

D
53 days

E
None of these

Solution

Apply work equivalence method.
Let the number of days be 'D'.
Now, according to this question,
= D = 63

Alternative: Chain Rule
Required number of days = 15 [(14/10) (18/6)] = 63 days
Question 9
1 / -0

A and B together can do a piece of work in 12 days, B and C together can do that work in 18 days, and A and C together can do the same work in 36 days. In how many days can they do five times the same work if all of them work together?

A
50 days

B
45 days

C
60 days

D
75 days

E
None of these

Solution

A and B can do the job in 12 days.
………(1)
B and C can do the job in 18 days.
………(2)
A and C can do the job in 36 days.
………(3)
On adding the three equations, we get
2 =
= 1/12 ………(4)
So, A, B and C can together finish the work in 12 days.
Therefore, five times the same work will be completed in 12 5 = 60 days.
Question 10
1 / -0

A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work for 10 days, then B and C leave. How many more days will A take to finish the work?

A
26 days

B
22 days

C
18 days

D
14 days

E
None of these

Solution

Let A, B and C take x, y and z days, respectively.
1/x + 1/y = 1/30 ………(1)
1/y + 1/z = 1/24 ………(2)
1/z + 1/x = 1/20 ...…....(3)
Solving these equations simultaneously, we get
1/x + 1/y + 1/z = 1/16 ...…….(4)
By solving (2) and (4), we get x = 48.
A, B and C together complete a job in 16 days.
In ten days, 10/16 of the job is completed and 6/16 of the job remains.
∵ x = 48, i.e. A completes 1/48 of the job in one day.
∴ A completes 6/16 of job in (6/16) 48 = 18 days
Question 11
1 / -0

If 5 men or 9 women can do a piece of work in 19 days, how long will it take to complete the same work with 3 men and 6 women?

A
15 days

B
4 days

C
6 days

D
12 days

E
None of these

Solution

5 men or 9 women (5 M = 9 W) can do the job = 19 days (Given) 3M = 27/5 W
3 men and 6 women = (27/5 + 6 ) = 57/5 women
Time taken by 57/5 women to complete the work = 19 9 5/57 = 15 days
Question 12
1 / -0

One tap can fill a cistern in 2 hours and another tap can empty the cistern in 3 hours. How long will it take to fill the cistern if both the taps are opened?

A
5 hours

B
6 hours

C
7 hours

D
8 hours

E
None of these

Solution

First pipe can fill cistern = 2 hours
Second pipe can empty the cistern = 3 hours
Now, according to question,
Time taken to fill the cistern = = 6 hours.
Question 13
1 / -0

A tank can be emptied by three taps in 3 hours. The first tap alone can empty it in 6 hours and second tap alone can empty it in 9 hours. How many hours will the third tap alone take to empty the tank?

A
12

B
15

C
18

D
20

E
None of these

Solution

Time taken by the first tap to empty the tank = 6 hours
Time taken by the second tap to empty the tank = 9 hours
Let the time taken by the third tap = 't' hr
According to the question,
1/6 + 1/9 + 1/t = 1/3
1/t = 1/3 - 1/6 - 1/9
1/t = (6 - 3 - 2)/18 = 1/18
t = 18 hours
Question 14
1 / -0

Two pipes A and B would fill a cistern in 37 min and 45 min, respectively. If both the pipes are opened, when should the second pipe be turned off so that the cistern may be filled in half an hour?

A
After 7 min

B
After 9 min

C
After 12 min

D
After 5 min

E
None of these

Solution

Pipe A can fill the tank in 37min = min
Pipe B can fill the tank in 45 min
Let the pipe B is turned off after y min
Now, according to question,
= 1 y = × 45 = × 45 = 9 min.
Question 15
1 / -0

A pumping set of 1.5 kilowatts (kW) can raise 1500 litres of water from a well of certain depth in certain time. A pumping set of how many kilowatts (kW) is needed to raise 4500 litres of water from the well of the same depth and in the same time?

A

B

C

D

E
None of these

Solution

By direct proportion, the required answer = = 4.5 kW
Question 16
1 / -0

If two pipes function simultaneously, the reservoir will be filled in 12 hours. The first pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?

A
35

B
20

C
28

D
25

E
30

Solution

Assume that the second pipe fills the reservoir in x hours.
Then, the first pipe can fill the reservoir in (x - 10) hours. Because pipe A fill the reservoir 10 hours faster than second.
According to the question,
=
(x - 10 + x) 12 = x² - 10x
24x - 120 = x² - 10x
x² - 34x + 120 = 0
x² - 30x + 4x + 120 = 0
(x - 30) (x - 4) = 0
x = 30, 4
But x 4 ( x - 10 should be positive.)
x = 30 hours
Question 17
1 / -0

Eina, Mina and Dika are three carpenters. They take a contract and start simultaneously to finish this task. Mina can finish the work in 16 days; Eina is twice as much efficient as Mina, whereas Dika is as much efficient as Mina. Eina and Mina leave after 2 and 4 days, respectively. How many more days will Dika take to finish the work?

A
4 days

B
6 days

C
8 days

D
12 days

E
3 days

Solution

Mina can finish the work in 16 days.
Eina is twice as much efficient as Mina. So, she can finish the work in 8 days.
Dika can finish the work in 16 days.
Assume that Dika will take x more days to finish the work.
Then, + + = 1
= 1
12 + x = 16
x = 4 days
It means that Dika will take 4 more days to finish the work.
Question 18
1 / -0

20 men could do a piece of work in 30 days working 4 hours a day, 30 men worked for 20 days for 3 hours a day. Then all were laid off, except one. How many more days would it take the last man to complete the remaining work, working 10 hours a day?

A
20

B
30

C
40

D
60

E
80

Solution

Let work done by 1 man in 1 hour = w
As 20 men, working 4 hours a day, take 30 days to get the work done,
Total work = 20 × 4 × 30 × w
Now, by working 3 hours a day, work accomplished by 30 men in 20 days = 3 × 30 × 20 × w
Work left to be done = (20 × 4 × 30 × w) - (3 × 30 × 20 × w) = 20 × 30 × w
Now, let the last man take d days to complete the work.
So, d × 10 × w = 20 × 30 × w
Or, d = 60
Thus, the last man would take 60 days.
Hence, answer option 4 is correct.
Question 19
1 / -0

It was estimated that 20 men would complete a work in 50 days working for 5 hours a day. But after 15 days from the start of work, 10 men dropped out of work. How many hours per day did the remaining men have to work to complete the work on time?

A
6

B
8

C
10

D
12

E
20

Solution

M₁D₁H₁ = M₂D₂H₂

20 50 5

= 20 15 5 + 10 35 H
H = 10 hours
Question 20
1 / -0

A and B worked together and completed a work in 24 days. They got some money for their work. If they distribute that money according to their work, A would get 50% more money than B. In how many days could B alone complete the work?

A
40

B
48

C
50

D
60

E
72

Solution

A gets 50% more money

A is 50% more efficient than B.

If B can do 'x' work in a day, A will do '1.5x' work in a day.

So, 1.5x + x = x =
This means that B can do ^thof the work in one day.
This means that B alone can complete whole work in 60 days.