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# Time & work

## TIME & WORK SET 8

Q.1 A piece of work can be done by 5 men or 9 women in 19 days. In how many days, will 3 men and 6 women complete the same piece of work? A) 15 days B) 4 days C) 6 days D) 12 days Ans. A Five men or 9 women (5 M = 9 W) can do the job = 19 days (Given)3M = 27/5 W3 men and 6 women = (27/5 + 6 = 57/5 women) 57/5 womenTime taken by 57/5 women to complete the work = 19 × 9 × 5/57 = 15 days. Q.2 A contractor undertook a certain work to be done in 80 days and employed 72 men to do it. After 20 days he found that 1/3rd of the work has been finished. How many men should he dismiss in order that the work may be finished on the date agreed upon?A) 48 menB) 72 menC) 24 menD) 36 men Ans. C72 person can finish rd of work in 20 days.It mean they can complete the remaining job in 40 days.Now according to the questions40 × 72 = (72 – x) 6072 – x = 48x = 24 To complete the work in 60 days, contractor has to reduce 24 men. Q.3 The time required by A to complete a piece of work is times the time required by B to complete the same piece of work. If A and B work together, they take 16 days less than the time taken by A alone to complete the piece of work. How many days will B alone take to complete the piece of work?A) 20 daysB) 40 daysC) 60 daysD) 80 daysAns. C Assume B can do the work in ‘d’ days.So, A needs d days.A and B together need = days.It is given – = 16d = 60 days. Q.4 ‘C’ can do as much work in 1 day, as A and B together can do in the same period of time. A alone can do the same piece of work in 12 days, whereas B alone can do it in 16 days. If B and C work together, how many days will they take to complete the piece of work?2A) 3 daysB) 4 daysC) 5 daysD) 3 daysAns. BA can do part of the work in 1 day.B can do part of the work in 1 day.So, C can do = part of the work in 1 day.So, B and C can do = in 1 day.So, it takes = 4 days. Q.5 Rahul is sailing at a uniform speed when a leak develops in his boat. He uses a bucket to empty water from the boat and reaches the shore in 30 minutes just in time to avoid sinking. The leak fills the boat twice as fast as the Rahul is able to empty it. Had the leak developed 10 minutes earlier how much faster would the Rahul have had to work to reach the shore safely?A) 20 %B) 25 %C) 30 %D) 35 %Ans. BLet r = rate of removing water from the boatthen2r = rate of water leaking into the boatlet a boat full of water, ready to sink = 130/r – 30/2r=12(30) – 30 = 2r60 – 30 = 2r30 = 2rr = 15 rate of removing water from the boat:Find the rate if leak occurs 10 min earlier (40 min to the shore)40/r-40/2r=12(40) – 40 = 2r2r = 40r = 20 rate of removing water from the boatI guess you could say remove the water; 5/15 = 33% faster Q.6 A does a work in 90 days, B in 40 days and C in 12 days. They work one after another for a day each, starting with A followed by B and then by C. If the total wages received is Rs. 360 and A, B and C share it in the ratio of the work done, find their respective individual wages. A) Rs. 40, Rs. 60 and Rs. 260B) Rs. 36, Rs. 81 and Rs. 243C) Rs. 42, Rs. 86 and Rs. 232D) None of theseAns. B 1/90+1/40+1/12=43/360 43*8/360=344/360 so 16/360 -1/90=1/40 1/40-1/30=1/120 1/120/1/12=1/10 9*1/90:9*1/40:81/10*1/12 4:9:27 4/40*360=369/40*360=8127/40*360=243 Q.7 In one day a man can do twice the amount of work done by a child in a day. It takes 40 days for 50 children working for 8 hours a day to complete the piece of work. If 40 men work for 5 hours a day, how many days will it take them to complete the same piece of work?A) 40 daysB) 60 daysC) 80 daysD) 10 daysAns. C 20 men is equivalent to 90 children.= = = d2 = 80 days. Q.8 In how many ways 19 people can be seated around two round tables with seating capacities of 9 & 10 people.A) 19!/9!B) 8!/9!C) 19C9*8!*9!D) 2*19C9*8!*9!Ans. DOut of two tables , 1 table can be selected in 2 ways.Out of 19 people , 9 people can be selected in 19C9 ways & 9 people can be arranged around a circular table in 9-1= 8! Ways.Also, 10 people can be arranged around a circular table in 10-1=9! Ways.Therefore, Total no. of ways=2*19C9*8!*9!

## TIME & WORK SET 7

Q.1 It was calculated that 75 men could complete a piece of work in 20 days. When work was scheduled to commence, it was found necessary to send 25 men to another project. How much longer will it take to complete the work? A) 30 B) 40 C) 50 D) 60 Ans. A Explanation:Before:One day work = 1 / 20One man’s one day work = 1 / ( 20 * 75)Now:No. Of workers = 50One day work = 50 * 1 / ( 20 * 75)The total no. of days required to complete the work = 1/ 30 or 30 days Q.2 A man was engaged on a job for 30 days on the condition that he would get a wage of Rs. 10 for the day he works, but he have to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end, he was absent for work for how many days ? A) 5 days B) 6 days C) 7 days D) 8 days Ans. CExplanation:The equation portraying the given problem is:10 * x – 2 * (30 – x) = 216 where x is the number of working days.Solving this we get x = 23Number of days he was absent was (30-23) i.e.7 days. Q.3 A contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. How many men should be increased, each working now for 10 hours daily, so that the work can be completed in time. A) 140 B) 150 C) 160 D) 170 Ans. B Explanation:One day’s work = 2 / (7 * 90)One hour’s work = 2 / (7 * 90 * 8)One man’s work = 2 / (7 * 90 * 8 * 75)The remaining work (5/7) has to be completed within 60 days, because the totalnumber of days allotted for the project is 150 days.So we get the equation(2 * 10 * x * 60) / (7 * 90 * 8 * 75) = 5/7 where x is the number of men workingafter the 90th day.We get x = 225Since we have 75 men already as given in the question,Then, 225-75= 150 Q.4 It takes Mr. Karthik y hours to complete typing a manuscript. After 2 hours, he was called away. What fractional part of the assignment was left incomplete? A) (y – 2) / y B) 1-y/2 * y C) y-2 D) None of the above Ans. A Explanation:To type a manuscript karthik took y hours.Therefore his speed in typing = 1/y.He was called away after 2 hours of typing.Therefore the work completed = 1/y * 2.Therefore the remaining work to be completed = 1 – 2/y.(i.e.) work to be completed = (y-2)/y Q.5 If 3 houses are to be painted, Mr. A can paint a house in 6 days (nos are not same) Mr. B can do the same in 8 days & Mr. C in 12 days. If Mr. A does the work for 8 days & leaves for vacation, & Mr. B continues the work for the next 6 days, for how many days should Mr. C work? A) 10 B) 11 C) 12 D) 13 Ans. B 1/6 * 8 + 1/8*6 + 1/12 * x =3Multiply by common denominator of 24 32+18+2x = 7250+2x=722x=22X=11

## TIME & WORK SET 6

Q.1 A can do a piece of work in 5 days & B in 6 days & C in 12 days, then how long will they take all together ?A) 2 2/9B) 1 1/9C) 3 3/9D) 4 4/9Ans. AShortcut:(A+B+C) = xyz / xy + yz + zx5 * 6 * 12 / 5*6 + 6*12 + 12*5= 360 / 30+72+60=2 2/9 Q.2 5 men can prepare 10 toys in 6 days working 6 hrs. Then in how many days can 12 men prepare 16 toys working 8 hrs a day ?A) 3 daysB) 4 daysC) 5 daysD) 6 daysAns. AShortcut:M1D1W2T1 = M2D2T2W15*6*16*6 = 12 * D2*8*10D2=5*6*16*6 / 12*10*8= 3 days Q.3 15 Men do ½ work in 20 days. In how many days will 20 men do the full work ? A) 15 days B) 40 days C) 30 days D) 20 days Ans. C Since, men & days are inversely proportional while work & days are directly proportional i.e. 20 : 15 ? 20 : X½ : 1 X = 15 * 1 * 20 / 20 * ½ = 30 days Q.4 If 4 men or 7 women can finish a work in 60 days, in How many days same work can be finished by 8 men & 7 women ?A) 18 daysB) 19 daysC) 20 daysD) 21 daysAns. C1/ 8/4*60 + 7/7*60= 1/8/240 + 7/420On solving= 20 Q.5 A Contractor undertook to do work in 60 days. He employed 50 men. After 40 days he found that only half of the work had been done. How many additional men he should employ so that the work may be done in time ?A) 50B) 45C) 40D) 35Ans. A60 days – 40 days=20 daysRemaining work = 1-1/2 = ½In 40 days, ½ work is done by the 50 menTherefore, 50 * 40In 20 days, 50*40/20 = 100No. of additional men = 100-50 = 50

## TIME & WORK SET 5

Q.1 A certain no. of men complete a work in 60 days. If there were 8 men more work could be finished in 10 days less. How many men were originally there ?A) 40B) 41C) 42D) 43Ans. AShortcut:No. of more men * (60-10) / 108*50/10=40 Q.2 A can do work in 7 days. If A does twice as much work as B in a given time, find how long A & B would take to do the work ?A) 4 2/4 daysB) 5 2/3 daysC) 4 2/3 daysD) 5 2/4 daysAns. CShortcut:A+B=xy/x+yi.e. 7*14/14+7= 4 2/3 days Q.3 10 men can finish a work in 10 days where it takes 12 women to finish it in 10 days. If 15 men & 6 women undertake to complete the work how many days will they take to complete it ?A) 5 daysB) 6 daysC) 7 daysD) 8 daysAns. A15 men=10*10/15=20/3 days6 women=12*10/6=20 days15men+6women=20/3 * 20 / 20/3+20 (we have used this formula: x*y/x+y)20*20/80=5 days Q.4 A,B & C can finish a work in 10,12 & 15 days. If B stops after 2 days how long would it take to A & C to finish the remaining work ?A) ½ workB) 1/3 workC) ¼ workD) 1/5 workAns. AShortcut:2 (1/10 + 1/15 + 1/12)Or 2*1/4=1/2 work Q.5 A is twice as good as workman as B. Together they finish in 14 days. In how many days can it be done by each separately ?A) 21 daysB) 22 daysC) 23 daysD) 24 daysAns. AShortcut:(Twice + one) = Thrice in 14 daysi.e. 14 * 3 = 42 daysor twice person = 42 / 2 = 21 days

## TIME & WORK SET 4

Q.1 Two workers A & B working together completed a job in 5 days. If A worked twice as efficiently as he actually did & B worked 1/3 as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone, A would require ? A) 7 ½ days B) 6 ¼ days C) 8 ¾ days D) 5 1/5 days Ans. B Let A & B completes the job in x & y daysThus, 1/x + 1/y = 1/5–iAfter changing efficiencies A would be able to complete the work in x/2 days & B in 3x daysTherefore, 2/x + 1/3y = 1/3—iiOn solving these two equations we will getX = 6 ¼ days Q.2 A & B can complete a job in 24 days. A alone can complete in 32 days. Both of them worked together for 8 days & then A left. The number of days B will take to complete the remaining job is : A) 32 days B) 128 days C) 64 days D) 16 days Ans. C 1/A + 1/B = 1/24 & 1/A = 1/321/B = 1/24-1/32= 1/96B = 96 daysNow, 8/32 +8+x / 96 = 1Or 24+8+x=96X=96-32= 64 Shortcut:vabi.e. v 16 * 9 = 12 days Q.3 Ashok started a business with an investment of Rs. 10000. After a few months Alok joined him with an investment of Rs. 12000. At the end of one year from the start they shared Alok total profit equally. After how long did join ?A) 2 monthsB) 3 monthsC) 4 monthsD) 5 monthsAns. A10000 * 12 / 12000 * x = 1:110 / x = 1:1X=10Therefore , he joined the business with Ashok after 2 months Q.4 X & Y started a business with an investment of Rs.20000 & Rs.24000. At the end of one year total profit they shared was Rs.1000 more than the difference in their profit shares. Find the total profit ?A) 1100B) 1200C) 1300D) 1400Ans. A20000 : 24000 = 5 : 6Let the total profit share be 5x & 6x5x + 6x = 6x – 5x + 1000Therefore, 11x = x+1000X=100Therefore, total profit = 6x+5x = 11xOr 11 * 100 = 1100 Q.5 A & B enter into the specification A puts in Rs. 50 & B puts in Rs. 45. At the end of 4 months A withdrew half his capital & at the end of 6 months B withdraw half of its capital. C then enters with a capital of Rs. 70. At the end of 12 Months in what ratio will the profit be divided ?A) 80 : 81 : 84B) 82 : 83 : 85C) 86 : 88 : 89D) 91 : 93 : 95Ans. AA = 50 * 4 + 50/2 * 8 : 45*6 + 45/2*6 : 70*6Or 400 :405:450=80:81:84

## TIME & WORK SET 3

Q.1 If 3 men & 5 women can do a piece of work in 8 days & 2 men & 7 children do the same piece of work in 12 days. How many women can do as much work in a day as 21 children ? A) 15 B) 10 C) 7 D) 12 Ans. B If in 8 days the work can be done by 3 men+5women Therefore, in 1 day the work can be done by 8 (3 men + 5 women)24 men + 40 women Again if in 12 days the work can be done by 2 men + 7 childrenTherefore, if in 1 day the work can be done 12 (2 men + 7 children)24 men + 84 children Work of 24 men & 40 women = work of 24 men & 84 children Work of 84 children = work of 40 women Work of 1 children = work of 40/84 women Therefore, work of 21 children = work of 40*21 / 84 women = work of 10 women Q.2 When Manish alone can do a piece of work , he takes 16 days more than the time taken by Manish & Anuj together to complete the work while Anuj takes 9 days more than the time taken by Manish & Anuj together to complete the work. What time Manish & Anuj together will take to complete the work ? A) 10 days B) 11 days C) 12 days D) 13 days Ans. C Q.3 Number of men can do a piece of work in 24 days. If there were 5 men less the work could be finished in 8 days more. How many men were initially present at the work ? A) 20 B) 21 C) 22 D) 23 Ans. A Shortcut :a(D + d) / di.e. 5 (24 + 10) / 8 = 5*32 / 8 = 20 Q.4 Sunil completes a work in 4 days where Dinesh completes the work in 6 days. Ramesh works 1 ½ times as fast as sunil. Three together can complete the work in: A) 1 5/12 B) 1 5/7 C) 1 3/8 D) 1 5/19 Ans. D Number of days taken by Ramesh = 4*2/3 = 8/3Thus, x=4, y=6, z=8/3Therefore, xyz / xy + yz +zx On Solving, we will get1 5/19 Q.5 Three persons undertake to complete a work inRs.1200. The first person can complete a work in 8 days, second person in 12 days & third person in 16 days. They complete the work with the help of fourth person in 3 days. What does the fourth person get ? A) Rs. 225 B) Rs. 250 C) Rs. 200 D) Rs. 180 Ans. A Let fourth person works in x daysThus, 1/8 + 1/12 + 1/16 + 1/x = 1/3Or 1/x = 1/3- 1/8 -1/12 – 1/16Or 16-6-4-3 / 48 = 3/48 = 1/16Or x=16Now, ratio of work done by first, second, third & fourth person= 1/8 : 1/12 : 1/16 : 1/16 = 6:4:3:3 Thus , Amount by fourth person is: 3/16 * 1200 = Rs.225

## TIME & WORK SET 2

Q.1 Carpenter A can make chair in 6hrs , Carpenter B in 7 hrs & Carpenter C in 8hrs. If each carpenter works for 8hrs per day, how many chairs will be made in 21 days ?A) 73B) 69C) 61D) 67Ans. AA can make in 21 days= 21*8/6 = 28 chairsB can make in 21 days = 21*8/7 = 28chairsC can make in 21 days=21*8/8 = 21 chairsTherefore total no. of chairs = 28+24+21 = 73chairs Q.2 A & B can complete work together in 5 days. If A works at twice his speed & B at half of his speed , this work can be finished in 4 days. How many days would it take for A alone to complete the job ?A) 10B) 15C) 12D) 18Ans. ALet A can do work in x days & B can do in y daysThus,1/x + 1/y = 1/5—i2/x + 1/2y = ¼—iiNow solve these two equations, we will get2/x + 1/2y=1/44/x + 1/y=1/21/y=1/2 -4/x—–iiiPut the value of 1/y in eq-i1/x+1/y = 1/51/x + ½-4/x = 1/51/x-4/x=1/5-1/2=2-5/10 =-3/10Thus on solving we get,X=10 Q.3 Amit & Saurabh can complete a piece of work in 15 days. If B alone takes 20 days to complete that work. Find the time taken by A alone to complete that work . A) 60 days B) 61 days C) 62 days D) 63 days Ans. A Shortcut:Xy / y-x15*20 / 20-15 = 60 days Q.4 20 men can complete the work in 40 days. When should 4 men leave so that the work may be finished in 48 days ? A) 8 days B) 10 days C) 4 days D) 6 days Ans. A Suppose 4 men leave after x daysTherefore, work done by 20 men in x days = x/40Remaining work = 1- x/4040-x / 40No. of remaining days = 48-xNo. of remaining men = 20-4 = 16If 20 men can do in 40 days 1 workTherefore, 1 men can do in 1 day= 1 / 20*40 16 men can do in 48-x days = 1*16*(48-x) / 20*40Therefore, 16*(48-x) / 20*40 = 40-x / 40192-4x = 200-5xX=8 Q.5 25 Men were employed to do a piece of work which they could finish in 20 days but the men dropped off by 5 at the end of every 10 days. In what time will the work be completed ? A) 23 ½ days B) 8 days C) 26 days D) 17 days Ans. A Work done by 25 men in 1 day = 1/20Therefore, work done by 25 men in 10 days = 1/20 * 10 = ½Therefore, no. of workers available after 10 days= 25-5 = 20Work done by 25 men in 1 day = 1/20Work done by 1 man in 1 day = 1 / 20*25Work done by 20 men in 10 days = 1/20 * 1/25 * 20 * 10=2/5Again, the no. of workers available after 20 days = 20-5 = 15Remaining work = 1 – ½ – 2/5 = 1/10Therefore, 1/20 work is done by 25 men in 1 day 1 work is done by 1 men in = 1*20*251/10 work is done by 15 men in = 1*20*25*1 / 15*10 = 10/3Therefore, total no. of days = 10+10+ 3 1/3=23 1/3

## TIME & WORK SET 1

Q.1 Lipika reads a book for 1 ¾ hours every day. She reads the entire book in 6 days. How many hours in all were required by her to read the book? A) 16 B) 17 C) 18 D) 19 Ans. D 13/4 * 6/1 13/2 * 3/1 = 39/2 Or 19 Q.2 Suman studies for 5 2/3 hours daily. She devotes 4 2/5 hours of her time for Science and Mathematics. How much time does she devote for other subjects? A) 1 13/15 B) 2 13/15 C) 1 12/15 D) 2 12/15 Ans. B Total time of Suman’s study =5 2/3 hr = 17/3 hr. Time devoted by her for Science and Mathematics = 2 4/5 = 14/5 hr Thus, time devoted by her for other subjects = 17/3 – 14/5 hr 17 * 5 / 15 – 14 * 3/ 15 = 43/15 hr = 2 13/15 hr Q.3 A can complete a work in 20 days & B in 30 days. A worked alone for 4 days & then B completed the remaining work along with C in 18 days. In how many days can C working alone complete the work ? A) 68 days B) 90 days C) 12 days D) 72 days Ans. B Work done by A = 4/20 = 1/5 Therefore remaining work = 1-1/5 = 4/5 Let C working alone can do work in x days Thus, 18/30 + 18/x = 4/5 Or 18(x+30) * 5 =4*30x 90x + 2700 = 120 x 30x = 2700 Or x=90 days Q.4 In a garrison, there was food for 1000 soldiers for one month. After 10 days, 1000 more soldiers joined the garrison. How long would the soldiers be able to carry on with the remaining food ? A) 25 days B) 20 days C) 15 days D) 10 days Ans. D Let the number of days be X Then as per the question:- 1000*(30-10) = (1000+1000)*X 1000*20 = 2000*x X= 20000/2000 X=10 Q.5 If 3 men & 4 boys complete a work in 7 days & 2 men & 3 boys do the same work in 10 days. In how many days will 3 men & 8 boys complete the same work ? A) 5 days B) 6 days C) 7 days D) 8 days Ans. A 3 men & 4 boys complete a work in 7 days 2 men & 3 boys complete a work in 10 days Therefore, 3 men + 4 boys / 2 men + 3 boys = 10 / 7 (Since there is inverse proportional in men & days) 21 men + 28 days = 20 men + 30 boys 1 man = 2 boys 3 men + boys = 6 boys + 4 boys = 10 boys 3 men + 8 boys = 6 boys + 8 boys = 14 boys Boys days 10 7 14 x Or 10 / 14 = x / 7 X = 5 days