Time And Work Test-1

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Time And Work Test-1

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Question 1
1 / -0.25

A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It can be done by 9 men and 15 women in how many days ?

A
3 days

B
4 days

C
5 days

D
6 days

E
None of these

Solution

To calculate the answer we need to get 1 man per day work and 1 woman per day work.
Let 1 man 1 day work =x
and 1 woman 1 days work = y.
=>6x+5y = 1/6
and 3x+4y = 1/10
On solving, we get x = 1/54 and y = 1/90
(9 men + 15 women)'s 1 days work =
(9/54) + (15/90) = 1/3
9 men and 15 women will finish the work in 3 days
Question 2
1 / -0.25

A works twice as fast as B. if both of them can together finish a work in 12 days, B alone can do it in.

A
40 days

B
27 days

C
36 days

D
24 days

E
None of these

Solution

Let time taken by b to do the work=2t
:a= t
1 day work of a and b = 1/2t+1/t=1+2/2t
=3/2t_(1)
1day work of a and b =1/12_(2)
1/12=3/2t
t=18
b can do that work alone =18×2=36
Question 3
1 / -0.25

A alone can complete a work in 12 days, while A and B together can complete the same work in 8 days. The number of days that B will take to complete the work alone is

A
10 days

B
24 days

C
20 days

D
9 days

E
None of these
Question 4
1 / -0.25

A work could be completed in 100 days. Due to the absence of 10 workers it was completed in 110 days. The original number of workers was

A
55

B
100

C
50

D
110

E
None of these
Question 5
1 / -0.25

A can do a job in 15 days B in 10 days and C in 30 days. If A is helped by B and C on every third day, the job will be completed in

A
9 days

B

C
8 days

D

E
None of these

Solution

Given:
Time taken by A = 10 days
Time taken by B = 15 days
Time taken by C = 30 days
B and C both assist on every third day
Formula used:
Work = Efficiency ×Time
Calculation:
LCM of 10, 15 and 30 is 30
Efficiency of A = (30/10) = 3 units/days
Efficiency of B = (30/15) = 2 units/days
Efficiency of C = (30/30) = 1 units/days
Work done by A on first two days = (3 ×2) = 6
Work done by A, B and C on third day = (3 + 2 + 1) = 6
Total work done by A, B and C in 3 days = (6 + 6) = 12
Similarly,
Work done by A, B and C in next three days = 12 units
Total work done by A, B and C in 6 days = (12 + 12) = 24 unit
Remaining work = (30 – 24) units = 6 units
Number of days taken by A to complete the remaining work = (6/3) = 2 days
Total days = (3 + 3 + 2) = 8 days
∴The required time is 8 days
Question 6
1 / -0.25

Certain number of men can complete a job in 30 days. If there were 5 more men, it could be completed in 10 days less. How many men were there in the beginning?

A
10

B
15

C
25

D
20

E
None of these
Question 7
1 / -0.25

A man is paid Rs. 20 for each day he works and loses Rs. 3 for each day he is idle. At the end of 60 days he gets Rs. 280. Then he was idle for

A
20 days

B
25 days

C
30 days

D
40 days

E
None of these

Solution

Suppose the worker remained idle for x days . Then , he worked for (60 −x) days.
∴        20(60 −x)−3x=280
⇔     1200-23x=280
⇔     23x=920
⇔       x=40
Question 8
1 / -0.25

A takes twice as much time as B or thrice as much time as C to finish a piece of work; working together they can finish the work in 2 days. In how many days B can do the work alone?

A
12 days

B
4 days

C
8 days

D
6 days

E
None of these

Solution

Suppose A, B and C takes x, x/2, x/3 days respectively to finish the work.

⇒12/2 = 6 Days.
Question 9
1 / -0.25

4 men and 6 women can complete a work in 8 days while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete the work.

A
50

B
45

C
40

D
35

E
None of these

Solution

The correct option is C.
Let 1 man 's 1 day 's work = x and 1 woman 's 1 day 's work = y.

Solving the two equations, we get:
x = , y =
∴ 1 woman 's 1 day 's work =
⇒ 10 women 's 1 day 's work = ( x 10) =
Hence, 10 women will complete the work in 40 days.
Question 10
1 / -0.25

72 men can build a wall 280 m long in 21 days. How many men will take 18 days to build a similar type of a wall of length 100 m.

A
28

B
18

C
10

D
30

E
None of these

Solution

The correct option is D.
Here work is 280 m length of wall and 100 m length of wall
Let 'M 'men finish the 100 m wall.
72 ×21/280 = M ×18/100
72 ×21/280=M ×18/100
M=30