Time and Work Test

Result

Time and Work Test - 4

Score
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Question 1
1 / -0

Two taps together can fill a cistern in 8 hours. If the first tap alone can fill it in 15 hours, then how much time will the second tap alone take to fill it?

A
hours

B
hours

C
hours

D
hours

Solution

Let the two taps be A and B.
According to question:

∴
Time taken by tap 'B' alone will be hours or hours.
Question 2
1 / -0

A, B and C complete a work in 3 days. A alone can do it in 8 days. B alone can also do the same work in 8 days. In how many days can C alone finish the same work?

A
4 days

B
12 days

C
8 days

D
24 days

Solution

'C' can finish the same work in 12 days.
Question 3
1 / -0

A and B together can do a piece of work in 15 days while B and C together can do the same work in 12 days and C and A together can do the same work in 10 days. They all work together for 5 days, then B and C leave. How many more days will A take to finish the remaining work?

A
18

B
12

C
10

D
9

E
7

Solution

Adding all the equations, we get

In 5 days, work completed =
Remaining work = 1 - =
Now,

work is done by A in 1 day.
∴ work will be done by A in = 9 days.

Required number of days = 9
Question 4
1 / -0

It was estimated that 30 men would complete a piece of work in 50 days, working for 6 hours a day. But after 15 days from the start of the work, 15 men dropped out of work. How many hours per day will the remaining men have to work so as to complete the work on time?

A
12 hours

B
10 hours

C
15 hours

D
20 hours

Solution

Let the work done by 1 man in 1 hour be w.
Let total work be W.
So, 30 × 50 × 6 × w = W
Work done in 15 days = 30 × 6 × 15 × w
Work left = 30 × 6 × w × (50 - 15) = 30 × 6 × w × 35
Number of men left to do the work = 15
Number of days left for the work to be completed = 50 - 15 = 35
Let 1 man now work for h hours per day.
So, 15 × h × 35 × w = 30 × 6 × w × 35
Or h = 12
Hence, option 1 is correct.
Question 5
1 / -0

Three pipes A, B and C together can fill a tank in 6 hours. If all three are kept open at the same time for 2 hours, after which C is closed, A and B can fill the remaining part of the tank in 7 hours. What is the number of hours taken by C alone to fill the tank?

A
10

B
12

C
14

D
16

E
None of these

Solution

2 hours' work:

Remaining part of tank to be filled = 1 - =
portion of the tank is filled in 7 hours.

Full tank is filled in hours.

= hours

According to the question,

∴

=
=

Pipe C alone fills the tank in 14 hours.
Question 6
1 / -0

15 men are employed to do a piece of work which they can finish in 10 days, but 5 men quit at the end of 5 days. In how many days will the remaining work be completed?

A
7.5 days

B
5 days

C
5.5 days

D
7 days

Solution

Let the work done by 1 man in 1 day be w.
As 15 men work for 10 days, total work = 15 × 10w = 150w
Now, work done by 15 men in 5 days = 15 × 5w = 75w
Thus, work left to be done by 10 men = 75w
Let these men take d days.
Work done by these 10 men in d days = d × w × 10 = 10dw
This must be equal to the remaining work.
Thus, 10dw = 75w or d = 7.5
Thus, the 10 remaining men will take 7.5 days to complete the work left.
Hence, answer option 1 is correct.
Question 7
1 / -0

'A' can do a piece of work in 9 days, 'B' can do the same work in double of that time and 'C' can only do 1/4^th of as much work as 'A' does in one day. How long will it take for 'A', 'B' and 'C' to do the same job if they all work together?

A
days

B
days

C
days

D
days

Solution

A's one day's work =
B's one day's work =
C's one day's work =

Total work will be completed in days.
days.
Question 8
1 / -0

Taps A, B and C can fill a tank in 12, 15 and 10 hours, respectively. If tap B is opened all the time and tap A and tap C are opened for one hour each alternately, the tank will be full in

A
hours

B
7 hours

C
hours

D
4 hours

Solution

, and
For 1^st hour, part of tank filled =

For 2^nd hour, part of tank filled =

Total tank filled in 2 hours =

Total tank filled in 6 hours =
Remaining portion of tank =

portion of tank will be filled in
= hours
Total tank is filled in hours.
Question 9
1 / -0

If 100 men can do 100 jobs in 100 days, then in how many days can 1 man can do 1 job?

A
1

B
50

C
100

D
150

Solution

100 men 100 days 100 jobs
1 man 1 day jobs
1 man 1 job 100 days
Question 10
1 / -0

A and B can do a work in 30 days and 10 days, respectively. If they work on alternate days, beginning with A, in how many days will the work be completed?

A
days

B
days

C
days

D
days

Solution

One day's work:
A = 1/30 part of total work
B = 1/10 part of total workTwo days' work (1^stday A, and 2^nd day B) =
14 days' work =
Remaining work =
15^th day's work =

Remaining work =
Now, B's turn:

Total work is completed in days.