Raashid Shah

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    

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    

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    

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    

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  

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