{"id":5984,"date":"2025-06-09T10:43:20","date_gmt":"2025-06-09T10:43:20","guid":{"rendered":"https:\/\/thecompanyboy.com\/?p=5984"},"modified":"2025-06-09T10:43:20","modified_gmt":"2025-06-09T10:43:20","slug":"rs-aggarwal-quantitative-aptitude-pdf-download-time-work-and","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/drive\/rs-aggarwal-quantitative-aptitude-pdf-download-time-work-and\/","title":{"rendered":"RS Aggarwal Quantitative Aptitude PDF Free Download: TIME AND WORK"},"content":{"rendered":"

TIME AND WORK<\/strong><\/h1>\n

II MPORTANT FACTS <\/u><\/strong>AND FORMULAE<\/u><\/strong><\/h2>\n
    \n
  1. If A can do a piece of work in n days, then A’s 1 day’s work = (1\/n)<\/li>\n
  2. If A\u2019s 1 day’s work = (1\/n),then A can finish the work in n days.<\/li>\n
  3. A is thrice as good a workman as B, then:<\/li>\n<\/ol>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Ratio of work done by A and B = 3 : 1.<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Ratio of times taken by A and B to finish a work = 1 : 3.<\/p>\n

    SOLVED EXAMPLES<\/h2>\n

    Ex. 1. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same Job.How long should it take both A and B, working together but independently, to do\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 the same job?<\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (IGNOU, 2003)<\/p>\n

    \u00a0\u00a0\u00a0 Sol.<\/strong> A\u2019s 1 hour’s work = 1\/8<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 B’s 1 hour’s work = 1\/10<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (A + B)’s 1 hour’s work = (1\/8) +(1\/10)=9\/40<\/p>\n

    Both A and B will finish the work in 40\/9 days.<\/p>\n

    Ex. 2. A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work? (Bank P.O. 2003)<\/strong><\/p>\n

    Sol<\/strong>. (A + B)’s 1 day’s work = (1\/4). A’s 1 day’s work = (1\/12).<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 B’s 1 day’s work =((1\/4)-(1\/12))=(1\/6)<\/p>\n

    \u00a0\u00a0\u00a0\u00a0 Hence, B alone can complete the work in 6 days.<\/p>\n

    Ex. 3. A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days<\/strong><\/p>\n

    of 7 bours each. How long will they take to do it, working together 8 hours a day?<\/strong>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong><\/p>\n

    Sol<\/strong>. A can complete the work in (7 x 9) = 63 hours.<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 B can complete the work in (6 x 7) = 42 hours.<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 A\u2019s 1 hour’s work = (1\/63) and B’s 1 hour’s work =(1\/42)<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (A + B)’s 1 hour’s work =(1\/63)+(1\/42)=(5\/126)<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0 Both will finish the work in (126\/5) <\/u>hrs.<\/p>\n

    Number of days. of (42\/5) hrs each =(126 x 5)\/(5 x 42)=3 days<\/p>\n

    Ex. 4. A and B can do a piece of work in 18 days; Band C can do it in 24 days A and C can do it in 36 days. In how many days will A, Band C finish it together and separately?<\/strong><\/p>\n

    Sol<\/strong>. (A + B)’s 1 day’s work = (1\/18)\u00a0\u00a0\u00a0 (B + C)’s 1 day’s work = (1\/24)<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 and (A + C)’s 1 day’s work = (1\/36)<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Adding, we get:\u00a0 2 (A + B + C)’s 1 day’s work =\u00ad(1\/18 + 1\/24 + 1\/36)<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =9\/72 =1\/8<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0 (A +B + C)’s 1 day’s work =1\/16<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0 Thus, A, Band C together can finish the work in 16 days.<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0 Now, A\u2019s 1 day’s work = [(A + B + C)’s 1 day’s work] – [(B + C)’s 1 day work:<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =(1\/16 \u2013 1\/24)= 1\/48<\/p>\n

    A alone can finish the work in 48 days.<\/p>\n

    Similarly, B’s 1 day’s work =(1\/16 \u2013 1\/36)=5\/144<\/p>\n

    B alone can finish the work in\u00a0 144\/5=28 4\/5 days<\/p>\n

    And C\u2019s 1 day work =(1\/16-1\/18)=1\/144<\/p>\n

    Hence C alone can finish the work in 144 days.<\/p>\n

    \u00a0<\/strong>Ex. 6. A is twice as good a workman as B and together they finish a piece<\/strong><\/p>\n

    in 18 days. In how many days will A alone finish the work?<\/strong><\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0 Sol<\/strong>. (A\u2019s 1 day\u2019s work):)(B\u2019s 1 days work) = 2 : 1.<\/p>\n

    (A + B)’s 1 day’s work = 1\/18<\/p>\n

    Divide 1\/18 <\/u>in the ratio 2 : 1.<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0 :. A\u2019s 1 day’s work =(1\/18*2\/3)=1\/27<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Hence, A alone can finish the work in 27 days.<\/p>\n

    Ex. 6. A can do a certain job in 12 days. B is 60% more efficient than A. How many<\/strong><\/p>\n

    days does B alone take to do the same job?<\/strong><\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0 Sol<\/strong>. Ratio of times taken by A and B = 160 : 100 = 8 : 5.<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Suppose B alone takes x days to do the job.<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0 Then, 8 : 5 :: 12 : x = 8x = 5 x 12 =x = 7 1\/2 days.<\/p>\n

    Ex. 7. A can do a piece of work in 80 days. He works at it for 10 days B alone finishes the remaining work in 42 days. In how much time will A and B working together, finish the work<\/strong>?<\/p>\n

    Sol. Work done by A in 10 days =(1\/80*10)=1\/8<\/p>\n

    Remaining work = (1- 1\/8) =7\/ 8<\/p>\n

    Now,7\/ 8 work is done by B in 42 days.<\/p>\n

    \u00a0Whole work will be done by B in (42 x 8\/7) = 48 days.<\/p>\n

    A\u2019s 1 day’s work = 1\/80 and B’s 1 day’s work = 1\/48<\/p>\n

    (A+B)’s 1 day’s work = (1\/80+1\/48)=8\/240=1\/30<\/p>\n

    Hence, both will finish the work in 30 days.<\/p>\n

    Ex. 8. A and B undertake to do a piece of work for 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 finish it in 3 days. !find the share of each.<\/strong><\/p>\n

    Sol :<\/strong>C’s 1 day’s work = 1\/3-(1\/6+1\/8)=24<\/p>\n

    \u00a0\u00a0\u00a0 A : B : C = Ratio of their 1 day’s work = 1\/6:1\/8:1\/24= 4 : 3 : 1.<\/p>\n

    \u00a0\u00a0 A\u2019s share = Rs. (600 *4\/8) = Rs.300, B’s share = Rs. (600 *3\/8) = Rs. 225.<\/p>\n

    \u00a0 C’s share = Rs. [600 – (300 + 225\u00bb) = Rs. 75.<\/p>\n

    Ex.\u00a0 9. A and B working separately can do a piece of work in 9 and 12 days respectively, If they work for a day alternately, A beginning, in how many days, the work will be completed?<\/strong><\/p>\n

    \u00a0(A + B)’s 2 days’ work =(1\/9+1\/12)=7\/36<\/p>\n

    Work done in 5 pairs of days =(5*7\/36)=35\/36<\/p>\n

    \u00a0\u00a0 Remaining work =(1-35\/36)=1\/36<\/p>\n

    \u00a0 On 11th day, it is A\u2019s turn. 1\/9 work is done by him in 1 day.<\/p>\n

    \u00a01\/36 work is done by him in(9*1\/36)=1\/4 day<\/p>\n

    Total time taken = (10 + 1\/4) days = 10 1\/4days.<\/p>\n

    Ex 10 .45 men can complete a work in 16 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?<\/p>\n

    (45 x 16) men can complete the work in 1 day.<\/p>\n

    1 man’s 1 day’s work = 1\/720<\/p>\n

    45 men’s 6 days’ work =(1\/16*6)=3\/8<\/p>\n

    \u00a0Remaining work =(1-3\/8)=5\/8<\/p>\n

    75 men’s 1 day’s work = 75\/720=5\/48<\/p>\n

    Now,5<\/u> work is done by them in 1 day.<\/p>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 48<\/p>\n

    5<\/u>work is done\u00a0 by them in (48<\/u> x 5<\/u>)=6 days.<\/p>\n

    8\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0 8\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

    Ex:11.\u00a0\u00a0 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days.In how many days can 2 men and 1 boy do the work?<\/p>\n

    Soln: Let 1 man\u2019s 1 day\u2019s work = x and 1 boy\u2019s 1 day\u2019s work = y.<\/p>\n

    Then, 2x+3y = 1<\/u> and 3x+2y = 1<\/u><\/h1>\n