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maths: time and work

1.
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

 A's 1 day's work = 1 ; 15

 B's 1 day's work = 1 ; 20

 (A + B)'s 1 day's work = 1 + 1 = 7 . 15 20 60

 (A + B)'s 4 day's work = 7 x 4 = 7 . 60 15

 Therefore, Remaining work = 1 - 7 = 8 . 15 15

 2 A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:

 (A + B + C)'s 1 day's work = 1 , 4

 A's 1 day's work = 1 , 16

 B's 1 day's work = 1 . 12 C's 1 day's work = 1 - 1 + 1 = 1 - 7 = 5 . 4 16 12 4 48 48

 So, C alone can do the work in 48 = 9 3 days. 5 5

 3 A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
 A's 2 day's work = 1 x 2 = 1 . 20 10

 (A + B + C)'s 1 day's work = 1 + 1 + 1 = 6 = 1 . 20 30 60 60 10

 Work done in 3 days = 1 + 1 = 1 . 10 10 5

 Now, 1 work is done in 3 days. 5 Whole work will be done in (3 x 5) = 15 days.

 4 A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
Ratio of times taken by A and B = 1 : 3.
The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.
 If difference of time is 60 days, B takes 3 x 60 = 90 days. 2

So, A takes 30 days to do the work.
 A's 1 day's work = 1 30

 B's 1 day's work = 1 90

 (A + B)'s 1 day's work = 1 + 1 = 4 = 2 30 90 90 45 A and B together can do the work in 45 = 22 1 days. 2 2

 5 A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
 C's 1 day's work = 1 - 1 + 1 = 1 - 7 = 1 . 3 6 8 3 24 24

 A's wages : B's wages : C's wages = 1 : 1 : 1 = 4 : 3 : 1. 6 8 24 C's share (for 3 days) = Rs. 3 x 1 x 3200 = Rs. 400. 24
 6 If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.
 Then, 6x + 8y = 1 and 26x + 48y = 1 . 10 2

 Solving these two equations, we get : x = 1 and y = 1 . 100 200

 (15 men + 20 boy)'s 1 day's work = 15 + 20 = 1 . 100 200 4 15 men and 20 boys can do the work in 4 days.

 7 A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
 A's 1 hour's work = 1 ; 4

 (B + C)'s 1 hour's work = 1 ; 3

 (A + C)'s 1 hour's work = 1 . 2

 (A + B + C)'s 1 hour's work = 1 + 1 = 7 . 4 3 12

 B's 1 hour's work = 7 - 1 = 1 . 12 2 12 B alone will take 12 hours to do the work.

 8 A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
 (A + B)'s 1 day's work = 1 10

 C's 1 day's work = 1 50

 (A + B + C)'s 1 day's work = 1 + 1 = 6 = 3 . .... (i) 10 50 50 25

A's 1 day's work = (B + C)'s 1 day's work .... (ii)
 From (i) and (ii), we get: 2 x (A's 1 day's work) = 3 25 A's 1 day's work = 3 . 50 B's 1 day's work 1 - 3 = 2 = 1 . 10 50 50 25

So, B alone could do the work in 25 days.

 9 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?
 Whole work is done by A in 20 x 5 = 25 days. 4

 Now, 1 - 4 i.e., 1 work is done by A and B in 3 days. 5 5

Whole work will be done by A and B in (3 x 5) = 15 days.
 A's 1 day's work = 1 , (A + B)'s 1 day's work = 1 . 25 15 B's 1 day's work = 1 - 1 = 4 = 2 . 15 25 150 75

 So, B alone would do the work in 75 = 37 1 days. 2 2

 10 A 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 them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?
 (P + Q + R)'s 1 hour's work = 1 + 1 + 1 = 37 . 8 10 12 120

 Work done by P, Q and R in 2 hours = 37 x 2 = 37 . 120 60

 Remaining work = 1 - 37 = 23 . 60 60

 (Q + R)'s 1 hour's work = 1 + 1 = 11 . 10 12 60

 Now, 11 work is done by Q and R in 1 hour. 60

 So, 23 work will be done by Q and R in 60 x 23 = 23 hours 2 hours. 60 11 60 11

So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.

 11 A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
 B's 10 day's work = 1 x 10 = 2 . 15 3

 Remaining work = 1 - 2 = 1 . 3 3

 Now, 1 work is done by A in 1 day. 18 1 work is done by A in 18 x 1 = 6 days. 3 3

 12 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 it?
Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.
 Then, 4x + 6y = 1 and 3x + 7y = 1 . 8 10

 Solving the two equations, we get: x = 11 , y = 1 400 400 1 woman's 1 day's work = 1 . 400 10 women's 1 day's work = 1 x 10 = 1 . 400 40

Hence, 10 women will complete the work in 40 days.

 13 A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?
 (A + B)'s 20 day's work = 1 x 20 = 2 . 30 3

 Remaining work = 1 - 2 = 1 . 3 3

 Now, 1 work is done by A in 20 days. 3

Therefore, the whole work will be done by A in (20 x 3) = 60 days.

 14 P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
P can complete the work in (12 x 8) hrs. = 96 hrs.
Q can complete the work in (8 x 10) hrs. = 80 hrs. P's1 hour's work = 1 and Q's 1 hour's work = 1 . 96 80

 (P + Q)'s 1 hour's work = 1 + 1 = 11 . 96 80 480

 So, both P and Q will finish the work in 480 hrs. 11 Number of days of 8 hours each = 480 x 1 = 60 days = 5 5 days. 11 8 11 11

 15 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
 1 woman's 1 day's work = 1 70

 1 child's 1 day's work = 1 140

 (5 women + 10 children)'s day's work = 5 + 10 = 1 + 1 = 1 70 140 14 14 7 5 women and 10 children will complete the work in 7 days.