Quantitative Aptitude - Problems on Time and Work
Important Things to know for solving Problems on Time and Work
1. If A can do a piece of work in n days, then A’s 1 day work = 1/n
2. If A’s 1 day’s work = 1/n, then A can finish the work in n days.
Example: If A can do a piece of work in 4 days,then A’s 1 day’s work = 1/4. If A’s 1 day’s work = 1/5, then A can finish the work in 5 days
3. If A is thrice as good workman as B,then: Ratio of work done by A and B = 3:1. Ratio of time taken by A and B to finish a work = 1:3
4. Definition of Variation: The change in two different variables follow some definite rule. It said that the two variables vary directly or inversely. Its notation is X/Y = k, where k is called constant. This variation is called direct variation. XY = k. This variation is called inverse variation.
5. Some Pairs of Variables:
6. Some Important Tips:
More Men - Less Days and Conversely More Day - Less Men.
Since the total work is assumed to be one(unit), the number of days required to complete the given work would be the reciprocal of one day’s work. Sometimes, the problems on time and work can be solved using the proportional rule ((man*days*hours)/work) in another situation.
7. If men is fixed,work is proportional to time. If work is fixed, then time is inversely proportional to men therefore,
Problems on Time and Work
1) If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?
Solution: From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
2) If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in
Solution: From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
3) If 5 women or 8 girls can do a work in 84 days. In how many days can 10 women and 5 girls can do the same work?
Solution: Given that 5 women is equal to 8 girls to complete a work
4) Worker A takes 8 hours to do a job. Worker B takes 10hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Solution: A’s one hour work = 1/8.
5) A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day?
Solution: Given that B alone can complete the same work in days = half the time
6) A is twice as good a workman as B and together they finish a piece of work in 18 days.In how many days will A alone finish the work.
Solution: if A takes x days to do a work then
7) A can do a certain work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?
Solution: Ratio of time taken by A & B = 160:100 = 8:5
8) A can do a piece of work n 7 days of 9 hours each and B alone can do it in 6 days of 7 hours each. How long will they take to do it working together 8 2/5 hours a day?
Solution: A can complete the work in (7*9) = 63 days
9) A takes twice as much time as B or thrice as much time to finish a piece of work. Working together they can finish the work in 2 days. B can do the work alone in ?
Solution: Suppose A,B and C take x,x/2 and x/3 hours respectively finish the
10) X can do ¼ of a work in 10 days, Y can do 40% of work in 40 days and Z can do 1/3 of work in 13 days. Who will complete the work first?
Solution: Whole work will be done by X in 10*4 = 40 days.
1) A and B undertake to do a piece of workfor Rs 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they can finish it in 3 days, Find the share of each?
Solution: C’s one day’s work = (1/3)-(1/6+1/8) = 1/24
2) A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work?
Solution: Work done by A in 10 days = 10/80 = 1/8
3) P,Q and R are three typists who working simultaneously can type 216 pages in 4 hours In one hour, R can type as many pages more than Q as Q can type more than P. During a period of five hours, R can type as many pages as P can during seven hours. How many pages does each of them type per hour?
Solution: Let the number of pages typed in one hour by P, Q and R be x,y and z respectively. Then
4) Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
Solution: Number of pages typed by Ronald in one hour = 32/6 = 16/3
5) Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both working together. If B worked alone, he would need 4 1/2 hours more to compete the job than they both working together. What time would they take to do the work together.
Solution: (1/(x+8))+(1/(x+(9/2))) = 1/x
6) A and B can do a work in12 days, B and C in 15 days, C and A in 20 days. If A,B and C work together, they will complete the work in how many days?
Solution: (A+B)’s one day’s work = 1/12;
7) A and B can do a work in 8 days, B and C can do the same wor in 12 days. A,B and C together can finish it in 6 days. A and C together will do it in how many days?
Solution: (A+B+C)’s one day’s work = 1/6;
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 how many days?
Solution:(A+B)’s one day’s work = 1/10;
9) A is thrice as good a workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
Solution:Ratio of times taken by A and B = 1:3.
Solution: Work Done by A n 10 days = 10/80 = 1/8
11) 45 men can complete a work in 16 days. Six days after they started working, so more men joined them. How many days will they now take to complete the remaining work?
Solution: M1*D1/W1 = M2*D2/W2
12) A is 50% as efficient as B. C does half the work done by A & B together. If C alone does the work n 40 days, then A,B and C together can do the work in:
Solution: A’s one day’s work:B’s one days work = 150:100 = 3:2
13) 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?
Solution: B’s 10 day’s work = 10/15 = 2/3
14) A can finish a work in 24 days, B n 9 days and C in 12 days. B & C start the work but are forced to leave after 3 days. The remaining work done by A in:
Solution: (B+C)’s one day’s work = 1/9+1/12 = 7/36
15) X and Y can do a piece of work n 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of work. How long did the work last?
Solution: work done by X in 4 days = 4/20 = 1/5
16) A does 4/5 of 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*5/4 = 25 days
17) A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work n 23 days. The number of days after which A left the work was
Solution: (A+B)’s one day’s work = 1/45+1/40 = 17/360
18) A can do a piece of work in 10 days, B in 15 days. They work for 5 days. The rest of work finished by C in 2 days. If they get Rs 1500 for the whole work, the daily wages of B and C are:
Solution: Part of work done by A = 5/10 = 1/2
19) A alone can complete a work in 16 days and B alone can complete the same in 12 days. Starting with A, they work on alternate days. The total work will be completed in how many days?
(a) 12 days (b) 13 days (c) 13 5/7 days (d)13 ¾ days
Solution: (A+B)’s 2 days work = 1/16 + 1/12 = 7/48
20) 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?
Solution: A’s two day’s work = 2/20 = 1/10
21) Seven men can complete a work in 12 days. They started the work and after 5 days, two men left. In how many days will the work be completed by the remaining men?
(A) 5 (B) 6 (C ) 7 (D) 8 (E) none
Solution: 7*12 men complete the work in 1 day.
22) 12 men complete a work in 9 days. After they have worked for 6 days, 6 more men joined them. How many days will they take to complete the remaining work?
(a) 2 days (b) 3 days (c) 4 days (d) 5days
Solution: 1 man’s 1 day work = 1/108
23) A man, a woman and a boy can complete a job in 3,4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in ¼ of a day?
Solution:(1 man + 1 woman)’s 1 days work = 1/3+1/4 = 7/12
24) 12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it is to be completed in 3 days.
(A) 15 (B) 18 (C) 22 (D) data inadequate
Solution: one man’s one day’s work = 1/48
25) Twelve children take sixteen days to complete a work which can be completed by 8 adults in 12 days. Sixteen adults left and four children joined them. How many days will they take to complete the remaining work?
(A) 3 (B) 4 ( C) 6 (D) 8
Solution: one child’s one day work = 1/192;
26) Sixteen men can complete a work in twelve days. Twenty four children can complete the same work in 18 days. 12 men and 8 children started working and after eight days three more children joined them. How many days will they now take to complete the remaining work?
(A) 2 days (B) 4 days ( C) 6 days (D) 8 days
Solution: one man’s one day’s work = 1/192
27) Twenty-four men can complete a work in 16 days. Thirty- two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working and worked for 12 days. How many more men are to be added to complete the remaining work in 2 days?
(A) 16 men (B) 24 men ( C) 36 men (D) 48 men
Solution: one man’s one day’s work = 1/384
28) 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?
(A) 35 days (B) 40 days ( C) 45 days (D) 50 days
Solution: Let 1 man’s 1 day’s work = x days and
29) One man, 3 women and 4 boys can do a piece of work in 96 hours, 2 men and 8 boys can do it in 80 hours, 2 men & 3 women can do it in 120 hours. 5 Men & 12 boys can do it in how many hours?
(A) 39 1/11 hrs (B) 42 7/11 hrs ( C) 43 7/11 days (D) 44hrs
Solution: Let 1 man’s 1 hour’s work = x
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