Test: Time And Work- 1


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QUESTION: 1

P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in

Solution:

Work done by P and Q in 1 day = 1/10

Work done by R in 1 day = 1/50

Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50

But Work done by P in 1 day = Work done by Q and R in 1 day .
Hence the above equation can be written as

Work done by P in 1 day * 2 = 6/50

⇒ Work done by P in 1 day = 3/50

⇒ Work done by Q and R in 1 day = 3/50

Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25

So Q alone can do the work in 25 days

QUESTION: 2

P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?

Solution:

Amount of work P can do in 1 day = 1/16

Amount of work Q can do in 1 day = 1/12 

Amount of work P, Q and R can together do in 1 day = 1/4

Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48

⇒ Hence R can do the job on 48/5 days = 9 +(3/5) days

QUESTION: 3

Machine P can print one lakh books in 8 hours. Machine Q can print the same number of books in 10 hours while machine R can print the same in 12 hours. All the machines started printing at 9 A.M. Machine P is stopped at 11 A.M. and the remaining two machines complete work. Approximately at what time will the printing of one lakh books be completed?

Solution:

(P + Q + R)'s 1 hour's work = (1 / 8 + 1 / 10 + 1 / 12) = 37 / 120.
Word done by P, Q and R in 2 hours = (37 / 120 x 2) = 37 / 60.
Remaining work = (1 - 37 / 60) = 23 / 60.
(Q + R)'s 1 hour's work = (1 / 10 + 1 / 12) = 11 / 60.
Now, 11 / 60 work is done by Q and R in 1 hour.
so, 23 / 60 work will be done by Q and R in (60 / 11 x 23 / 60) = 23 / 11 hour ≈ 2 hour.
So, the work will be finished approximately 2 hours after 11 A.M.,i.e.,around 1 P.M.

QUESTION: 4

6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in ____ days.

Solution:

Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b 

Work done by 6 men and 8 women in 1 day = 1/10 

⇒ 6m + 8b = 1/10

⇒ 60m + 80b = 1    (1)

Work done by 26 men and 48 women in 1 day = 1/2 

⇒ 26m + 48b =1/2

⇒ 52m + 96b = 1    (2)

Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200

Work done by 15 men and 20 women in 1 day 

= 15/100 + 20/200 =1/4

⇒ Time taken by 15 men and 20 women in doing the work = 4 days

QUESTION: 5

A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?

Solution:

Whole work is done by A in (20 x 5 / 4) = 25 days.
Now, (1 - 4 / 5) i.e., 1 / 5 work is done by A and B in 3 days.
Whole work will be done by A and B in (3 x 5) = 15 days.
A's 1 days's work = 1 / 25,
(A + B)'s 1 day's work = 1 / 15.
∴ B's 1 day work = (1 / 15 - 1 / 25) = 4 / 150 = 2 / 75. 
So, B alone would do the work in 75 / 2 = 37 x 1 / 2 days.

QUESTION: 6

P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. how many days does P alone need to finish the remaining work?

Solution:

Work done by P in 1 day = 1/18
Work done by Q in 1 day = 1/15
Work done by Q in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6

QUESTION: 7

A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?

Solution:

C's 1 day's work = 1 / 3 - (1 / 6 + 1 / 8) = 1 / 3 - 7 / 24 = 1 / 24
A's wages : B's wages : C's wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1.
∴ C's share (for 3 days) = Rs. (3 x 1 / 24 x 3200) = Rs. 400.

QUESTION: 8

P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?

Solution:

Amount of work P can do in 1 day = 1/20
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60

P is working alone and every third day Q and R is helping him

Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5

So work completed in 15 days = 5 × 1/5 = 1

Ie, the work will be done in 15 days

QUESTION: 9

P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?

Solution:

Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 x (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15

QUESTION: 10

To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

Solution:

We have,

B = 3/2*A
A = 2/3*B
One day's work, (A+B) = 1/18
(2/3*B+B) = 1/18
5/3*B = 1/18
One day's work of B = 3/90
B alone can complete the work in,
= 90/3 = 30 days.

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