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Time And Work |

**Important Time and Work Formula**

Knowing the formulae allows you to jump right to a solution after reading the question. As a result, understanding the formula for any numerical ability issue simplifies the solution and computations.

Work Done = Time Spent x Work Rate

Work Rate = 1 / Time Required

Time taken = 1 / Work Rate

If a piece of work takes x days to complete, the work completed in one day equals 1/x.

Number of Days x Total Wok Done = Efficiency

Efficiency and time are inversely related. If X:y is the ratio of the number of workers necessary to perform a piece of labour, then y:x is the ratio of the time spent to complete the task.

If x people can perform W1 work in D1 days while working T1 hours per day, and y individuals can do W2 work in D2 days while working T2 hours per day, the relationship between them will be.

**The primary types of questions that may be asked in the test with respect to time and job topic are listed below:**

to determine a person's efficiency

To determine how long it takes an individual to complete a task

To determine how long it takes a group of people to execute a task

Individual work completed in a set amount of time

Work completed by a group of people over a period of time.

Source: Safalta.com

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**Questions and answers:**

**Question 1:**

**Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days?**

**Option 1: 11**

**Option 2: 12**

**Option 3: 13**

**Option 4: 14**

**Answer:**

**3: 13**

**Explanation:**

**Let a man can finish the job alone in 'x' days'**

**In one day work of the man is '(1/x)' days.**

**2 machine take time to finish the work = 13 days So, 1 machine take time to finish the work = 13 x 2 = 26 days**

**1 day work of the machine (1/26) days**

**According to the questions,**

**3/M+8/26=2(8/M + 3/26)**

**⇒3/M + 4/13 = 16/M + 3/26**

**⇒16/M-3/M = 4/13-3/13**

**⇒13/M = 1/13**

**⇒M=169**

**A man complete the work in '169' days.**

**So, number of men required to complete the work in 13 days=169/13 = 13 men**

**:: The number of men required to complete the work in 13 days is 13 men.**

**Question 2:**

**At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?**

**Option 1: 12**

**Option 2: 18**

**Option 3: 24**

**Option 4: 36**

**Answer:**

**2: 18**

**Explanation:**

**Men × day = total work**

**A and B together finish a task in 12 days.**

**A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does,**

**the task would have been completed in 9 days.**

**According to the question,**

**⇒ (A + B)× 12 = (A/2 + 3B)× 9**

**⇒ 12A + 12B = (9/2)A + 27B**

**⇒ (12 – 9/2)A = (27 – 12)B**

**⇒ 15A = 30B**

**⇒ A/B = 2/1**

**A efficiency is 2 unit work in a day, B efficiency is 1 unit work in a day**

**⇒ total work = (A + B)× 12**

**⇒ (2 + 1)× 12**

**⇒ 36 unit**

**A take to finish the task if she works alone at her usual efficiency**

**⇒ 36/2**

**⇒ 18 days**

**∴ A take to finish the task if she works alone at her usual efficiency would be 18 days.**

**Question 3:**

**A piece of work is carried out by a group of men, all of equal capacity, in such a way that on the first day one man works and on every subsequent day one additional man joins the work. A group of women, all of equal capacity is engaged to carry out a second piece of work with ten women starting the work on the first day and one woman leaving the work at the end of everyday. The second piece of work requires three times the effort required for the first piece of work and each man is thrice as efficient as each woman. It is known that one man working alone can complete the first piece of work in 6 days.**

**I. Number of days in which the second piece of**

**work is completed.**

**II. Number of days in which the first piece of**

**work is completed.**

**Option 1: if I>I|**

**Option 2: if II>I**

**Option 3: If1=11**

**Option 4: if the relationship cannot be determined from the given information**

**Answer: **

**1: if1>11**

**Explanation:**

**Question 4:**

**A dye company received an order of 400 litres of black dye and 360 litres of brown dye. It has two machines - X and Y - to make these dyes. X takes 4 hours to make 16 litres of black dye and 3 hours to make 9 litres of brown dye. Y takes 4 hours to make 12 litres of black dye and 3 hours to make 12 litres of brown dye. If the company has to deliver the order in 93 hours, the delivery will be delayed by at least**

**Option 1: 227 hours**

**Option 2: 237 hours**

**Option 3: 247 hours**

**Option 4: 257 hours**

**Answer:**

**4: 257 hours**

**Explanation:**

**Question 5: **

**Time taken by 3 boys and 2 girls to complete the work is 4 days. The work done by 5 girls is 7 days more than the work done by 4 boys. The number of days in which work is completed when a boy and a girl is working together is -**

**Option 1: 110/9 days**

**Option 2: 120/11 days.**

**Option 3: 60/7 days**

**Option 4: 113/18 days.**

**Answer:**

**2: 120 / 11 days**

**Explanation:**

**Let 1 day's work by a boy and 1 day's work by a girl be 1/a and 1/b respectively.**

**⇒ 3/a + 2/b = 1/4**

**⇒ a/5 + 7 = b/4**

**Solving,**

**⇒ a = 15 and b = 40**

**Girl's 1 day's work = 1/15**

**Boy's 1 day's work = 1/40**

**(Boy + Girl)'s 1 day's work = 1/15 + 1/40 = 11/120**

**∴ In 120/11 days can complete the work when a boy and a girl working together**

**Question 6:**

**A takes 20% more days than B to complete the work, when they work alone. To complete 1/4th of work, A alone works. A and B works together to complete 1/2th of the work. Remaining work gets completed by B in 5 days. Find the number of days in which total work gets completed. **

**Option 1: 18.4 days**

**Option 2: 14.4 days**

**Option 3: 16.4 days**

**Option 4: 20.4 days**

**Answer:**

**3: 16.4 days**

**Explanation:**

**Remaining work completed by B = 1 - 1/2 - 1/4 = 1/4**

**Number of days in which B alone can complete the work = 4 × 5 = 20**

**A alone can complete the work in = 20 × 120/100 = 24 days**

**⇒ A's 1 day's work = 1/24**

**⇒ B's 1 day's work = 1/20**

**⇒ (A + B)'s 1 days work = 1/24 + 1/20 = 11/120**

**1/4 of the work gets completed by A in = 1/4 × 24 = 6 days**

**1/2 of the work completed by A and B in = 1/2 × (120/11) = 60/11 days**

**∴ Total time in which work gets completed = 6 + 60/11 + 5 = 181/11 ≈ 16.4 days**

**Question 7:**

**Three friends A, B and C worked together to complete the work. A takes 4 days more to complete same work done by A and B. Work done by C in 4 days is equal to the work done by A in one day. Work done by B in 3 days is equal to the work done by C in 8 days. Find the time in which work will be completed if all three worked together.**

**Option 1: 120/23 days.**

**Option 2: 110/23 days.**

**Option 3: 130/23 days.**

**Option 4: 140/23 days.**

**Answer :**

**1: 120/23 days.**

**Explanation:**

**Let number of hours taken by A, B and C to complete the work be a, b and c respectively.**

**⇒ 3/b = 8/c**

**⇒ 3c = 8b**

**⇒ 4/c = 1/a**

**⇒ c = 4a**

**⇒ b = 3a/2**

**⇒ 1/a + 1/b = 1/(a - 4)**

**⇒ 1/a + 2/3a = 1/(a - 4)**

**⇒ a = 10**

**⇒ b = 15**

**⇒c = 40**

**(A + B + C)'s 1 hours work = 1/10 + 1/15 + 1/40 = 23/120**

**∴ Working together, A, B and C can complete the work in 120/23 days.**

**Question 8:**

**Working together, A and B can complete 9% of work per hours. When A worked for 4 hours and B worked for 5 hours then 40% of work is completed. Find the difference between the number of hours taken by alone B and alone A to complete the work. **

**Option 1: 10 hours**

**Option 2: 5 hours**

**Option 3: 8 hours**

**Option 4: 12 hours**

**Answer:**

**2: 5 hours**

**Explanation:**

**Working efficiency of A and B when they worked together = 9% per hour**

**Let working efficiency of A be a% per hour.**

**Working efficiency of B = (9 - a)% per hour**

**⇒ 4 × a + 5 × (9 - a) = 40**

**⇒ 4a + 45 - 5a = 40**

**⇒ a = 5%**

**Working efficiency of B = 9 - 5 = 4% per hour**

**Number of hours in which A alone can complete the work = 100/5 = 20 hours**

**Number of hours in which B alone can complete the work = 100/4 = 25 hours**

**∴ Required difference = 25 - 20 = 5 hours**

**Question 9: **

**M and N can complete the work in 30 days and 20 days respectively. They worked together, but after some days M left the work and N complete the remaining work in 15 days. In how many days work will be completed? **

**Option 1: 12 days**

**Option 2: 15 days**

**Option 3: 18 days**

**Option 4: 24 days**

**Answer:**

**3: 18 days**

**Explanation: M's 1 day's work = 1/30**

**N's 1 day's work = 1/20**

**(M + N)'s 1 days work = 1/30 + 1/20=1/12**

**Let number of days for which M works for be a days.**

**N completed fraction of work = 15/20 = 3/4**

**Work completed by M and N in a days = 1-3/4=1/4**

**M and N worked for = 1/4 x 12 = 3 days**

**:: Number of days in which work will be completed = 3+15= 18 days**

**Question 10:**

**Two diamond mining machines each working 12 hours per day for 8 days handles 9 tons on diamond with an efficiency of 90%. While 3 other diamond mining machines at an efficiency of 80% set to handle 12 tons of coal in 6 days. How many hours per day each should work?**

**Option 1: 12 hours**

**Option 2: 14 hours**

**Option 3: 16 hours**

**Option 4: 18 hours**

**Answer:**

**3: 16 hours**

**Explanation:**

**By Chain Rule:**

**(N, × Dg × Hg × Ej)/WG = (N2 × D2 X H2 × E2)/W2**

**= ( 2 × 8 × 12 × 90) / 9 = (3 x 6xH 80 ) / 12**

**= 1920 = 120xH2**

**→H2 = 1920/120**

**H2 = 16 hours**

**.. Each should work for 16 hours per day.**

**Question 11:**

**Three pipes named Pipe A, Pipe B and Pipe C are using to fill/drain a tank. It takes 15 hrs to fill the tank if only Pipe A and Pipe B opened. And it will take 20 hrs if Pipe A and Pipe B are used to fill the tank and Pipe C to drain. How much time will it take if all pipes used to fill the tank?**

**Option 1: 6 hrs**

**Option 2: 8 hrs**

**Option 3: 10 hrs**

**Option 4: 12 hrs**

**Answer:**

** 4: 12 hrs**

**Explanation:**

**1/A + 1/B = 1/15 ---(1)**

**1/A + 1/B - 1/C = 1/20 ---(2)**

**(1) - (2) gives**

**⇒ 1/C = 1/15 - 1/20 = 4/60 - 3/60 = 1/60**

**1/A + 1/B + 1/C = 1/15 + 1/60 = 5/60 = 1/12**

**12 hrs is needed to fill the tank if all the pipes were opened.**

**Question 12:**

**Arjun, Bablu and Charan together make a total of 10 chairs in one day. Together, they were assigned the job of making a total of 100 chairs. Initially, Arjun started the work, without Bablu and Charan joining him. After a few days, Arjun quit, and immediately Bablu and Charan took over and together they completed the job after a few more days. If it took a total of 20 days to complete the entire work and Arjun makes at least 6 chairs per day, then, how many days did Arjun work on the job?**

**Option 1: 8**

**Option 2: 10**

**Option 3: 12**

**Option 4: 15**

**Answer:**

** 2:10**

**Explanation:**

**Suppose the number of chairs which can be made by each of Arjun, Bablu and Charan in a day be x, y and z,**

**respectively.**

**Let us say Arjun worked alone for d days.**

**According to question –**

**Case I:**

**⇒ (x + y + z) = 10**

**Case II:**

**⇒ xd + (20 – d)(y + z)= 100**

**⇒ xd + (20 – d)(10 – x) = 100**

**⇒ xd + 200 – 10d – 20x + dx = 100**

**⇒ 2xd – 10d + 100 – 20x = 0**

**⇒ 2d(x – 5)+ 20(5 – x) = 0**

**⇒ 2d(x – 5) – 20(x – 5)= 0**

**⇒ (x – 5)(2d – 20) = 0**

**⇒ x = 5 and d = 20/2 = 10**

**Given that x ≥ 6**

**∴ x ≠ 5**

**∴ d = 10 days**

**Therefore, Arjun worked for 10 days.**

**Question 13: **

**Prakash, Varun and Gajini had to paint three identical fences. On the first day, only Prakash turned up for work and he completed the work only on the first fence, taking m hours. On the second day, all three of them turned up for work and they completed the work only on the second fence, taking (m – 4) hours. On the third day, Varun and Gajini turned up and they completed the work on the third fence, taking (m+ 5) hours. What is the value of m? **

**Option 1: 8**

**Option 2: 6**

**Option 3: 10**

**Option 4: 9**

**Answer:**

**3: 10**

**Explanation:**

**Question 14: **

**Lalit and Mohan are working on an assignment. Lalit takes 8 hours to type 36 pages on a computer, while Mohan takes 12 hours to type 45 pages on a computer. How much time will they take, working together on two different computers to type an assignment of 132 pages? **

**Option 1: 14 hours**

**Option 2: 15 hours**

**Option 3: 16 hours**

**Option 4: 18 hours**

**Answer:**

**3: 16 hours**

**Explanation:**

**Number of pages that Lalit can type per hour == 4.5 pages/hour**

**Number of pages that Mohan can type per hour == 3.75 pages/hour So, Number of Pages typed by both Lalit& Mohan together= (4.5+ 3.75) pages/hr**

**= 8.25 pages/hr**

**=pages/hr 132 hours**

**.. Time taken by both to type 132 pages = 132/33/4**

**= 16 hours.**

**Question 15: **

**A is as efficient as B and C together. Working together A and B can complete a work in 36 days and C alone can complete it in 60 days. A and C work together for 10 days. B alone will complete the remaining work in: **

**Option 1: 88 days**

**Option 2: 110 days**

**Option 3: 121 days**

**Option 4: 99 days**

**Answer:**

** 2: 110 days**

**Explanation:**

** efficiency of A= efficiency of (B+C)**

**A+B= 5**

**C= 3**

**Work done by A and C = 7 × 10 = 70**

**Remaining work by B = (180 − 70)/1 = 110 days**

**Question 16: **

**A building is built by X, Y and Z, who are able to build it alone in 8, 12 and 10 days respectively. Each day along with X, Y works for half day, while Z works 2/3 rd of the day. If after 4 days X and Z stopped working, then find the time taken by Y to build the remaining building while working 1/15 of a day? **

**Option 1: 16 days**

**Option 2: 18 days**

**Option 3: 8 days**

**Option 4: 12 days**

**Answer: **

**4: 12 days**

**Explanation:**

**Total work = 120 Units**

**Work done by X, Y, Z in 4 days**

**= [15+ (10) + (12)] × 4 X**

**= (15+5+8) x 4 = 112 Units**

**Remaining work = 120-112 = 8 Units**

**Days taken by Y = 8 /1/15 (10) = 12 days**

**Question 17: **

**If A and B can complete a work together in 20 days, and A alone can do the same work in 32 days. When both work together their efficiencies reduce by 20% compare to the efficiency when they would have worked alone. Find the number of days B alone takes to complete the same work?**

**Option 1: 32 days**

**Option 2: 24 days**

**Option 3: 30 days**

**Option 4: 36 days**

**Answer:**

**1: 32 days**

**Explanation:**

**A and B takes 20 days with 80% efficiency.**

**With 100% efficiency they would take 20 × 80/100 = 16 days.**

**Efficiency of B = 2 – 1 = 1**

**Number of days taken by B alone = 32/1 = 32 days**

**Question 18:**

**Ajay works at a rate such that he can finish a piece of work in 48 days. But he works at this rate for 32 days only. Later, he works at a rate such that he can do the whole work in 40 days. How many days will he take to finish the whole work?**

**Option 1: 48 days**

**Option 2: 4234 days**

**Option 3: 4513 days**

**Option 4: 4712 days**

**Answer: **

**3: 4513 days**

**Explanation:**

**Let total work be 240 units**

**Units**

**work done by Ajay in first 32 days = 32 x 5 = 160 units**

**Remaining work =240-160 =80 units **

**Time taken do to remaining work = 80/6 = 13 1/3 days**

**Total time = 32 + 13 1/3 = 45 1/3 days**

**Question 19: **

**A can complete a certain piece of work in 25 days. B is 20% more efficient than A and C is 35% more efficient than B. They work together for 5 days. The half of the remaining work will be completed by A alone in ?**

**Option 1: 21920 days**

**Option 2: 21720 days**

**Option 3: 21520 days**

**Option 4: 21320 days**

**Answer:**

**1: 21920 days**

**Explanation:**

**Let efficiency of A = 100**

**Total work done by A= 50 x 25**

**= 1250**

**In 1 day, work done by A, B & C = 191**

**In 5 days = 955**

**Remaining work = 1250-955**

**= 295**

**Half of the remaining work will be completed by A alone in= 295/(2x50) days**

**= 21920 days**

**Question 20:**

**A & B can finish the job in 8 days. If A worked 200% more efficiently & B worked 6623% less efficiently the work is completed in 6 days. Find time in which A would finish the work. **

**Option 1: 2123 days**

**Option 2: 2113 days**

**Option 3: 2013 days.**

**Option 4: 2023 days**

**Answer: **

**2: 2113 days**

**Explanation:**