Download Time and Work Questions for CAT<\/a><\/p>\n Enroll to CAT Mocks at just Rs. 299<\/a><\/p>\n Question 1:\u00a0<\/b>Anil can paint a house in 12 days while Barun can paint it in 16 days. Anil, Barun, and Chandu undertake to paint the house for \u20b9 24000 and the three of them together complete the painting in 6 days. If Chandu is paid in proportion to the work done by him, then the amount in INR received by him is<\/p>\n 1)\u00a0Answer:\u00a03000<\/b><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Now Anil Paints in 12 Days Question 2:\u00a0<\/b>Mira and Amal walk along a circular track, starting from the same point at the same time. If they walk in the same direction, then in 45 minutes, Amal completes exactly 3 more rounds than Mira. If they walk in opposite directions, then they meet for the first time exactly after 3 minutes. The number of rounds Mira walks in one hour is<\/p>\n 2)\u00a0Answer:\u00a08<\/b><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Considering the distance travelled by Mira in one minute = M,<\/p>\n The distance traveled by Amal in one minute = A.<\/p>\n Given if they walk in the opposite direction it takes 3 minutes for both of them to meet. Hence 3*(A+M) = C. (1)<\/p>\n C is the circumference of the circle.<\/p>\n Similarly, it is mentioned that if both of them walk in the same direction Amal completes 3 more rounds than Mira :<\/p>\n Hence 45*(A-M) = 3C. (2)<\/p>\n Multiplying (1)*15 we have :<\/p>\n 45A + 45M = 15C.<\/p>\n 45A – 45M = 3C.<\/p>\n Adding the two we have A = $\\frac{18C}{90}$<\/p>\n Subtracting the two M = $\\frac{12C}{90}$<\/p>\n Since Mira travels $\\frac{12C}{90}$ in one minute, in one hour she travels :$\\frac{12C}{90}\\cdot60\\ =\\ 8C$<\/p>\n Hence a total of 8 rounds.<\/p>\n Alternatively,<\/p>\n Let the length of track be L Question 3:\u00a0<\/b>One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is<\/p>\n a)\u00a011.5<\/p>\n b)\u00a010<\/p>\n c)\u00a012.5<\/p>\n d)\u00a012<\/p>\n 3)\u00a0Answer\u00a0(B)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Let Rahul work at a units\/hr and Gautam at b units\/hour Question 4:\u00a0<\/b>Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then the tank becomes full at 6 pm. If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is<\/p>\n a)\u00a0144<\/p>\n b)\u00a0140<\/p>\n c)\u00a0264<\/p>\n d)\u00a0120<\/p>\n 4)\u00a0Answer\u00a0(A)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Let A fill the tank at x liters\/hour and B drain it at y liters\/hour Question 5:\u00a0<\/b>Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 days, Bimal and Charu join him. Together, they complete the painting in 14 more days. If they are paid a total of \u20b9 21000 for the job, then the share of Charu, in INR, proportionate to the work done by him, is<\/p>\n a)\u00a09000<\/p>\n b)\u00a09200<\/p>\n c)\u00a09100<\/p>\n d)\u00a09150<\/p>\n 5)\u00a0Answer\u00a0(C)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Let Entire work be W Checkout: CAT Free Practice Questions and Videos<\/strong><\/a><\/em><\/p>\n Question 6:\u00a0<\/b>Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is<\/p>\n 6)\u00a0Answer:\u00a032<\/b><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Let the total work be 48 units. Let Amar do ‘m’ work, Akbar do ‘k’ work, and Anthony do ‘n’ units of work in a month.<\/p>\n Amar and Akbar complete the project in 12 months.\u00a0Hence, in a month they do\u00a0$\\frac{48}{12}$=4 units of work.<\/p>\n m+k = 4.<\/p>\n Similarly, k+n = 3, and m+n = 2.<\/p>\n Solving the three equations, we get\u00a0$m=\\frac{3}{2},\\ k=\\frac{5}{2},\\ n=\\frac{1}{2}$.<\/p>\n Here, Amar works neither the fastest not the slowest, and he does 1.5 units of work in a month. Hence, to complete the work, he would take\u00a0$\\frac{48}{1.5}=32$months.<\/p>\n Question 7:\u00a0<\/b>Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works everyday. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is<\/p>\n a)\u00a05<\/p>\n b)\u00a08<\/p>\n c)\u00a06<\/p>\n d)\u00a07<\/p>\n 7)\u00a0Answer\u00a0(D)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n Let the total amount of work be 60 units.<\/p>\n Then Anu, Vinu, and Manu do 4, 5, and 3 units of work per day respectively.<\/p>\n On the 1st day, Anu and Vinu work. Work done on the 1st day = 9 units<\/p>\n On the 2nd day, Manu and Vinu work. Work done on the 2nd day = 8 units<\/p>\n This cycle goes on. And in 6 days, the work completed is 9+8+9+8+9+8 = 51 units.<\/p>\n On the 7th day, again Anu and Vinu work and complete the remaining 9 units of work. Thus, the number of days taken is 7 days.<\/p>\n Question 8:\u00a0<\/b>Two circular tracks T1 and T2 of radii 100 m and 20 m, respectively touch at a point A.\u00a0Starting from A at the same time, Ram and Rahim are walking on track T1 and track T2\u00a0at speeds 15 km\/hr and 5 km\/hr respectively. The number of full rounds that Ram will\u00a0make before he meets Rahim again for the first time is<\/p>\n a)\u00a05<\/p>\n b)\u00a03<\/p>\n c)\u00a02<\/p>\n d)\u00a04<\/p>\n 8)\u00a0Answer\u00a0(B)<\/strong><\/p>\n View Video Solution<\/a><\/p>\n Solution:<\/b><\/p>\n To complete one round Ram takes 100m\/15kmph and Rahim takes 20m\/5kmph<\/p>\n They meet for the first time after L.C.M of (100m\/15kmph , 20m\/5kmph) = 100m\/5kmph=20m\/kmph.<\/p>\n Distance traveled by Ram =20m\/kmph * 15kmph =300m.<\/p>\n So, he must have ran 300\/100=3 rounds.<\/p>\n Note:<\/strong><\/p>\n CAT gave both 2 and 3 as correct answers because of the word ‘before<\/strong>‘.<\/p>\n Question 9:\u00a0<\/b>A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other. Ram and Rahim reach their destination in one minute and four minutes, respectively. if they start at the same time, then the ratio of Ram’s speed to Rahim’s speed is<\/p>\n a)\u00a0$\\frac{1}{2}$<\/p>\n b)\u00a0$\\sqrt{2}$<\/p>\n c)\u00a0$2$<\/p>\n d)\u00a0$2\\sqrt{2}$<\/p>\n
\nBarun paints in 16 Days
\nNow together Arun , Barun and Chandu painted in 6 Days
\nNow let total work be W
\nNow each worked for 6 days
\nSo Anil’s work = 0.5W
\nBarun’s work =\u00a0$\\frac{6W}{16}=\\frac{3W}{8}$
\nTherefore Charu’s work =\u00a0$\\frac{W}{2}-\\frac{3W}{8}=\\ \\frac{W}{8}$
\nTherefore proportion of charu =$\\frac{24000}{8}=\\ 3,000$<\/p>\n
\nand velocity of Mira be a and Amal be b
\nNow when they meet after 45 minutes Amal completes 3 more rounds than Mira
\nso we can say they met for the 3rd time moving in the same direction
\nso we can say they met for the first time after 15 minutes
\nSo we know Time to meet = Relative distance \/Relative velocity
\nso we get $\\frac{15}{60}=\\frac{L}{a-b}$ \u00a0 \u00a0 (1)
\nNow When they move in opposite direction
\nThey meet after 3 minutes
\nso we get $\\frac{3}{60}=\\frac{L}{a+b}$ \u00a0\u00a0 (2)
\nDividing (1) and (2)
\nwe get $\\frac{\\left(a+b\\right)}{\\left(a-b\\right)}=5$
\nor 4a =6b
\nor a = 3b\/2
\nNow substituting in (1)
\nwe get :
\n$\\frac{L}{b}\\times\\ 2=\\ \\frac{15}{60}$
\nso $\\frac{L}{b}\\ =\\frac{1}{8}$
\nSo we can say 1 round is covered in $\\frac{1}{8}$ hours
\nso in 1-hour total rounds covered = 8.<\/p>\n
\nNow as per the condition :
\n8a+6b =7.5a+7.5b
\nso we get 0.5a=1.5b
\nor a=3b
\nTherefore total work = 8a +6b = 8a +2a =10a
\nNow Rahul alone takes 10a\/10 = 10 hours.<\/p>\n
\nNow as per Condition 1 :
\nWe get Volume filled till 10pm = 8x-7y \u00a0 \u00a0 \u00a0 (1) .
\nHere A operates for 8 hours and B operates for 7 hours .
\nAs per condition 2
\nWe get Volume filled till 6pm = 4x-2y \u00a0 \u00a0 \u00a0\u00a0 (2)
\nHere A operates for 4 hours and B operates for 2 hours .
\nNow equating (1) and (2)
\nwe get 8x-7y =4x-2y
\nso we get 4x =5y
\ny =4x\/5
\nSo volume of tank =\u00a0$8x-7\\times\\ \\frac{4x}{5}=\\frac{12x}{5}$
\nSo time taken by A alone to fill the tank = $\\frac{\\frac{12x}{5}}{x}=\\frac{12}{5}hrs\\ $
\n= 144 minutes<\/p>\n
\nNow Anil worked for 24 days
\nBimal worked for 14 days and Charu worked for 14 days .
\nNow Anil Completes W in 60 days
\nso in 24 days he completed 0.4W
\nBimal completes W in 84 Days
\nSo in 14 Days Bimal completes = $\\frac{W}{6}$
\nTherefore work done by charu = $W-\\frac{W}{6}-\\frac{4W}{10}$= $\\frac{26W}{10}$=$\\frac{13W}{30}$
\nTherefore proportion of Charu = $\\frac{13}{30}\\times\\ 21000$=9100<\/p>\n![](\"https:\/\/cracku.in\/media\/uploads\/image_lmGqNsE.png\")
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