- Staff Selection Commission Mathematics 1999 to 2017 - TIME AND WORK Part 4

Staff Selection Commission Mathematics - TIME AND WORK TYPE-III



Ans .

(2)20


  1. Explanation :

    (2) Using Rule 1,
    Let the original number of carpenters be x.
    =>M1D1=M2D2
    =>x * 9 = (x-5) * 12
    =>9x = 12x-60
    =>3x = 60 => x = 20





Ans .

(2)16 days


  1. Explanation :

    (2) Using Rule 1,
    =>2 men + 3 women = 4 men => 2 men = 3 women \ 3 men + 3 women = 5 men =>M1D1=M2D2
    => 4 * 20 = 5 *D2
    =>D2=\( \frac{4*20}{5} \) =16 days.





Ans .

(1)12 hours


  1. Explanation :





Ans .

(4)3 days


  1. Explanation :





Ans .

(4)8


  1. Explanation :


    => \( \frac{9}{10} \)=\( \frac{(x-1)(x+1)}{(x+2)(x-1))} \)=\( \frac{x+1}{x+2} \)
    =>10x + 10 = 9x + 18
    => x = 18-10 = 8





Ans .

(3)8 hrs.


  1. Explanation :

    (3) Using Rule 1,
    =>M1D1T1=M2D2T2
    =>80*16*6 = 64*15*T2
    =>T2 =\( \frac{80*16*6}{64*15} \)=8 hours.





Ans .

(1)16 days


  1. Explanation :

    (1) Using Rule 1,
    =>M1D1=M2D2
    =>18 * 24 = 27 * D2
    D2=\( \frac{18*24}{27} \)= 16 days.





Ans .

(3)43\( \frac{7}{11} \) hours


  1. Explanation :





Ans .

(3)x2/y days


  1. Explanation :

    (3) Using Rule 1,
    =>M1D1= M2D2
    => x.x = y.D2
    =>D2= x2/y days.





Ans .

(2)15 days


  1. Explanation :

    Using Rule 1,
    =>M1D1= M2D2
    => 30 * 18 = 36 * D2
    =>D2= \( \frac{30*18}{36} \) = 15 days.





Ans .

(1)10 days


  1. Explanation :

    1) 20 men = 24 women
    => 5 men = 6 women
    => 30 men + 12 women
    = 40 men
    =>M1D1= M2D2
    => 20 * 20 = 40 * D2
    D2=\( \frac{20*20}{40} \)= 10 days.





Ans .

(3)34 days


  1. Explanation :





Ans .

(4)20 days


  1. Explanation :

    (4) 3 * 5 men + 7 * 5 women
    = 4 * 4 men + 6 * 4 women
    => 16 men - 15 men = 35 women - 24 women
    =>1 man = 11 women
    => 3 men + 7 women = 40 women
    =>M1D1= M2D2
    => 40 * 5 = 10 * D2
    =>D2 = 20 days.





Ans .

(4)30


  1. Explanation :





Ans .

(2)100


  1. Explanation :

    (2) Using Rule 1,
    200 men do \( \frac{1}{4} \) work in 50 days.





Ans .

(2)56


  1. Explanation :





Ans .

(2)\( \frac{125}{49} \)


  1. Explanation :





Ans .

(1)300


  1. Explanation :

    (1) Using Rule 1,
    =>M1D1 =M2D2
    =>75 * 90 = M2*18
    =>M2=\( \frac{75*90}{18} \)=375
    => Number of additional men = 375-75 = 300.





Ans .

(3)5 days


  1. Explanation :

    (*) 4 men = 8 women
    => 1 man = 2 women
    => 6 men + 12 women
    => 12 women + 12 women = 24 women
    =>M1D1 =M2D2
    => 8 * 15 = 24 * D2
    =>D2 =\( \frac{8*15}{24} \)= 5days.





Ans .

(1)8


  1. Explanation :

    =>M1D1 =M2D2
    =>24 * 17 = M2*51
    =>M2 =\( \frac{24*17}{51} \) =8 men.



TYPE-VII



Ans .

(2)₹60


  1. Explanation :

    2) Ratio of Suman`s and Sumati`s 1 days work = \( \frac{1}{3} \):\( \frac{1}{2} \) =2:3
    Sum of the ratios = 2 + 3 = 5
    Suman`s share =\( \frac{2}{5} \)*150=₹60.





Ans .

(2)₹200.20


  1. Explanation :

    (2) Total wages of 500 workers = 500 × 200 = 100000
    Now, according to question,
    Correct Average =\( \frac{100000-180-20+80+220}{500} \)
    => \( \frac{100100}{500} \) =₹200.20.





Ans .

(3)₹750


  1. Explanation :

    (3) Using Rule 25,
    C`s 1 days work =\( \frac{1}{4} \)-(\( \frac{1}{8} \)+\( \frac{1}{12} \))=\( \frac{1}{4} \)-(\( \frac{3+2}{24} \))
    =>\( \frac{1}{4} \)-\( \frac{5}{24} \)=\( \frac{6-5}{24} \)=\( \frac{1}{24} \)
    =>A : B : C =\( \frac{1}{8} \):\( \frac{1}{12} \):\( \frac{1}{24} \)=3:2:1
    => C's share =₹(\( \frac{1}{6} \)*4500)=₹750.





Ans .

(3)₹9450


  1. Explanation :





Ans .

(2)₹400


  1. Explanation :

    (2) Using Rule 25,
    A`s 1 days work =\( \frac{1}{6} \)
    B`s 1 days work =\( \frac{1}{8} \) and (A + B + C)s 1 days work =\( \frac{1}{3} \)
    C`s 1days work =\( \frac{1}{3} \)-\( \frac{1}{6} \)-\( \frac{1}{8} \)=\( \frac{8-4-3}{24} \)=\( \frac{1}{24} \)
    Ratio of their one day’s work respectively=\( \frac{1}{6} \):\( \frac{1}{8} \):\( \frac{1}{24} \)=4:3:1
    Sum of the ratios = 4 + 3 + 1 = 8
    => C`s share =\( \frac{1}{8} \)*3200=₹400.





Ans .

(4)₹12,000


  1. Explanation :

    (4) A`s 1 days work =\( \frac{1}{15} \)
    B`s 1 days work =\( \frac{1}{10} \)
    Ratio =\( \frac{1}{15} \):\( \frac{1}{10} \)=2:3
    Sum of the ratios = 2 + 3 = 5
    A`s share =₹(\( \frac{2}{5} \)*300000) =₹12,000.





Ans .

(4)₹40


  1. Explanation :

    (4) Man : boy = 3 : 1
    Boys share = \( \frac{1}{4} \)*800 = 200.
    The daily wages of boy=₹(\( \frac{200}{5} \))=₹40.





Ans .

(2)₹250


  1. Explanation :





Ans .

(2)₹600


  1. Explanation :

    (2) Using Rule 25,
    Ratio of wages of A, B and C respectively
    = 5 * 6 : 6 * 4 : 4 * 9
    = 30 : 24 : 36 = 5 : 4 : 6
    Amount received by A =\( \frac{5}{5+4+6} \)*1800
    =\( \frac{5}{15} \)*1800=₹600.





Ans .

(3)4


  1. Explanation :

    (3) Total salary for 20 days= (75 × 20) = 1500
    Actual salary received = 1140
    Difference = (1500 – 1140) = 360
    Money deducted for 1 day’s absencefrom work= (15 + 75) = 90
    Number of days he was absent =\( \frac{360}{90} \)=4 days.





Ans .

(3)₹275


  1. Explanation :

    (3) Using Rule 25,
    First mans 1 days work =\( \frac{1}{7} \)
    Second mans 1 days work =\( \frac{1}{8} \)
    Let, Boys 1 days work =\( \frac{1}{x} \)
    =>\( \frac{1}{7} \)+\( \frac{1}{8} \)+\( \frac{1}{x} \)=\( \frac{1}{3} \)
    =>\( \frac{1}{x} \) = \( \frac{1}{3} \)-\( \frac{1}{7} \)-\( \frac{1}{8} \)
    =>\( \frac{56-24-21}{168} \)=\( \frac{11}{168} \)
    => Ratio of their one days work=\( \frac{1}{7} \):\( \frac{1}{8} \):\( \frac{11}{168} \)=24:21:11
    =>Sum of the ratios = 24 + 21 + 11= 56
    => Boy`s share in wages =\( \frac{11}{56} \)*1400 =₹275.





Ans .

(4)₹17,100


  1. Explanation :

    (4) 5 men = 7 women
    [Both earn same amount in 1 day]
    7 men =\( \frac{7}{5} \)*7 =\( \frac{49}{5} \) women
    7 men + 13 women
    =>\( \frac{49}{5} \)+13 =\( \frac{114}{5} \) women
    Now,7 women = 5250 => \( \frac{114}{5} \) women
    =>\( \frac{5250}{7} \)*\( \frac{114}{5} \)=₹17,100.





Ans .

(1)₹400


  1. Explanation :

    (1) According to the question,
    (2 × 14) men + 14 women
    = 16 men + 32 women
    =>(28 – 16) men =(32–14) women
    => 12 men = 18 women
    => 2 men = 3 women
    1 woman =\( \frac{2}{3} \)man
    Amount received by 1 woman per day= \( \frac{2}{3} \)*600=₹400.





Ans .

(3)₹160


  1. Explanation :

    (3) Using Rule 25,
    Work done by the third person in 1 day=\( \frac{1}{8} \)-\( \frac{1}{16} \)-\( \frac{1}{24} \)=\( \frac{6-3-2}{48} \)=\( \frac{1}{48} \)
    Ratio of their 1 day’s work=\( \frac{1}{16} \):\( \frac{1}{24} \):\( \frac{1}{48} \)=3:2:1
    Share of the third person =\( \frac{1}{3+2+1} \)*960=\( \frac{960}{6} \)
    =>₹160.





Ans .

(1)6:5


  1. Explanation :

    (1) Using Rule 25,
    Required ratio = 15 * 22 : 11 * 25 = 6 : 5





Ans .

(4)₹12000


  1. Explanation :

    (4) Expert`s 1 days work=\( \frac{1}{12} \)-\( \frac{1}{36} \)-\( \frac{1}{48} \)
    =>\( \frac{12-4-3}{144} \)=\( \frac{5}{144} \)
    Ratio of their respective work for 1 day =\( \frac{1}{36} \):\( \frac{1}{48} \):\( \frac{5}{144} \)=4:3:5
    Experts share =\( \frac{5}{12} \)*28800=₹12000.





Ans .

(1)₹300


  1. Explanation :

    (1) Using Rule 25,
    According to the question
    \( \frac{1}{15} \) +\( \frac{1}{12} \) +\( \frac{1}{C} \) =\( \frac{1}{5} \)
    Let C1s work in day be \( \frac{1}{C} \)
    \( \frac{1}{C} \)=\( \frac{1}{5} \)-\( \frac{1}{15} \)-\( \frac{1}{12} \)=\( \frac{12-4-5}{60} \)=\( \frac{1}{20} \)
    =>A:B:C=\( \frac{1}{15} \):\( \frac{1}{12} \):\( \frac{1}{20} \)=4:5:3
    => C`s share =\( \frac{3}{12} \)*1200 = ₹300.





Ans .

(4)12 days


  1. Explanation :

    (4) A`s 1 days work = \( \frac{1}{21} \)
    B`s 1 days work = \( \frac{1}{28} \)
    Total work done by both=\( \frac{1}{21} \)+\( \frac{1}{28} \)=\( \frac{4+3}{84} \)=\( \frac{1}{12} \)
    Amount is sufficient to pay 12 days wages of both.





Ans .

(4)₹400


  1. Explanation :

    (4) Rule 2 and Rule 25,
    Work done by A and B in 5 days = 5(\( \frac{1}{12} \)+\( \frac{1}{15} \))
    =5(\( \frac{5+4}{60} \))=\( \frac{9}{12} \)=\( \frac{3}{4} \)
    Time taken by C in doing \( \frac{1}{4} \)work = 5 days
    C will complete in 20 days.
    Ratio of wages = \( \frac{1}{12} \):\( \frac{1}{15} \):\( \frac{1}{20} \)
    =>5:4:3
    Amount received by A= \( \frac{5}{12} \)*960 = ₹400





Ans .

(2)₹20


  1. Explanation :

    (2) The daily earning of 'C' = Daily earning of (A + C) and (B + C) - Daily earning of (A + B + C) = 94 + 76 - 150 = 20





Ans .

(3)₹225


  1. Explanation :

    (3) Rule 3 and Rule 25,
    If the fourth person completes the work in x days, then
    \( \frac{3}{8} \)+\( \frac{3}{12} \)+\( \frac{3}{16} \)+\( \frac{3}{x} \)=1
    =>\( \frac{1}{x} \) = \( \frac{1}{3} \)-\( \frac{1}{8} \)-\( \frac{1}{12} \)-\( \frac{1}{16} \)
    =>\( \frac{16-6-4-3}{48} \) =>\( \frac{1}{16} \)
    x = 16
    Ratio of wages =\( \frac{1}{8} \):\( \frac{1}{12} \):\( \frac{1}{16} \):\( \frac{1}{16} \)=6:4:3:3
    Sum of ratios = 6 + 4 + 3+3 = 16
    Fourth person`s share =\( \frac{3}{16} \)*1200=₹225.





Ans .

(1) A : 150, B : 100, C : 150


  1. Explanation :

    (1) Rule 3 and Rule 25,
    If C alone completes the work in x days, then
    \( \frac{1}{16} \)+\( \frac{1}{24} \)+\( \frac{1}{x} \)=\( \frac{1}{6} \)
    => \( \frac{1}{x} \) = \( \frac{1}{6} \)-\( \frac{1}{16} \)-\( \frac{1}{24} \)
    =>\( \frac{8-3-2}{48} \)=\( \frac{1}{16} \)
    =>x = 16 days
    Ratio of their remuneration =\( \frac{1}{16} \):\( \frac{1}{24} \):\( \frac{1}{16} \)= 3:2:2
    A`s remuneration =\( \frac{3}{8} \)*400 = ₹150
    B`s remuneration =\( \frac{2}{8} \)*400 =₹100
    C`s remuneration =\( \frac{3}{8} \)*400 =₹150
    => A : 150, B : 100, C : 150





Ans .

(4)143.50

  1. Explanation :

    (4) Using Rule 25,
    Skilled : half skilled : unskilled =\( \frac{1}{3} \):\( \frac{1}{4} \):\( \frac{1}{6} \)
    =>(\( \frac{1}{3} \)*12) :(\( \frac{1}{4} \)*12):(\( \frac{1}{6} \)*12)
    = 4 : 3 : 2 Share of the trained labourer =\( \frac{28}{(7*4+8*3+2*10)} \) *369 =\( \frac{28}{28+24+20} \)*369
    =>\( \frac{28}{72} \)*369 =143.50.





Ans .

(2)₹100


  1. Explanation :

    (2) Work done by B= 1-\( \frac{19}{23} \) = \( \frac{23-19}{23} \) = \( \frac{4}{23} \)
    (A + C) : B = \( \frac{19}{23} \):\( \frac{4}{23} \) =19:4
    Sum of ratios = 19 + 4 = 23
    B`s share =\( \frac{4}{23} \)*575 =₹100





Ans .

(4)5 hours


  1. Explanation :

    Rate of earning of the man = 2000/50 = Rs. 40 per hour
    Rate of earning for additional hours = 40 × 3/2 = Rs. 60 per hour
    Let the man has to work for n additional hours.
    Then, 2000 + n × 60 = 2300
    ⇒ n × 60 = 300
    ⇒ n = 5h.





Ans .

(3)Rs.120


  1. Explanation :

    (3) (2 men + 1 woman)s 14 days work = (4 women + 2 men)s 8 days work
    => 28 men + 14 women
    => 32 women + 16 men
    => (28 - 16) = 12 men
    => (32 - 14) = 18 women
    => 2 men = 3 women
    1 woman = \( \frac{2}{3} \) man
    => Wages per day of 1 man = Rs. 180
    => Wages per day of 1 woman\( \frac{2}{3} \)*180 =Rs.120.





Ans .

(1)Rs. 67.50


  1. Explanation :

    (1) Time taken by A =\( \frac{63}{3.50} \)= 18 days
    Time taken by B =\( \frac{75}{2.5} \) =30 days.
    (A + B)s 1 days work =\( \frac{1}{18} \)+\( \frac{1}{30} \) = \( \frac{5+3}{90} \) =\( \frac{8}{90} \) = \( \frac{4}{45} \)
    Required time =\( \frac{45}{4}\) days
    Total wages =\( \frac{45}{4}\) * (3.50 + 2.50)
    =>Rs(\( \frac{45}{4}\)*6) = )Rs. 67.5.





Ans .

(3) Rs.250


  1. Explanation :

    (3) Ratio of A`s and B`s 1 days work =\( \frac{1}{12} \):\( \frac{1}{15} \) = 15:12 => 5:4
    Sum of the terms of ratio = 5 + 4 = 9
    A`s share = Rs.(\( \frac{5}{9} \)*450) = Rs.250.





Ans .

(1)Rs. 200


  1. Explanation :

    (1) Part of work done by C
    => 1- \( \frac{7}{11} \)-\( \frac{4}{11} \)
    => Total amount received = Rs. 550
    => C`s share = Rs(\( \frac{4}{11} \)*550) =Rs. 200.





Ans .

(1)Rs.50


  1. Explanation :

    (1) Let C alone complete the work in x days.
    According to the question,
    \( \frac{1}{5} \)+\( \frac{1}{15} \)+\( \frac{1}{x} \)=\( \frac{1}{3} \)
    =>\( \frac{1}{x} \) =\( \frac{1}{3} \)-\( \frac{1}{5} \)-\( \frac{1}{15} \)
    =>\( \frac{5-3-1}{15} \) =>\( \frac{1}{15} \)
    \ => x = 15 days = Time taken by C alone.
    Ratio of the 1 day’s work of A, B and C =\( \frac{1}{5} \):\( \frac{1}{15} \):\( \frac{1}{15} \) => 3:1:1
    Sum of the terms of ratio = 3 + 1 + 1 = 5
    C’s share = Rs(\( \frac{1}{5} \)*250) => Rs.50





Ans .

(1) Man ₹2.75, Woman ₹2.25


  1. Explanation :

    (1) Let daily wages of a man be Rs. x
    Daily wages of a woman = Rs.(x-\( \frac{1}{2} \))
    According to the question, 600x + 400(x-\( \frac{1}{2} \))
    = 1000 × 2.55
    => 600x + 400x - 200 = 2550
    => 1000x = 2550 + 200 = 2750
    => x=\( \frac{2750}{1000} \) =Rs. 2.75
    => Daily wages of a woman
    =>Rs. (2.75 – 0.5)
    =>Rs. 2.25



TYPE-VIII



Ans .

(1) 10


  1. Explanation :

    (1) Let initially the number of men
    be x.
    => According to question,
    M1D1W2 = M2D2W1
    x*30 = (x + 5)*(30 - 10)
    x*30 = 20x + 100
    30x - 20x = 100
    10x = 100
    x = 10





Ans .

(4) 8


  1. Explanation :

    (4) Using Rule 1,

    => 450*10*5*x
    = 625*8*6*6
    => x = \( \frac{625*8*6*6}{450*10*5} \) = 8





Ans .

(1) 24 days


  1. Explanation :

    (1) Work done by A in 15 days
    = \( \frac{1}{60} \)*15 = \( \frac{1}{4} \)
    Remaining work = 1-\( \frac{1}{4} \) = \( \frac{3}{4} \)
    Now, \( \frac{3}{4} \) work is done by B in 30
    days
    Whole work will be done by B in
    \( \frac{30*4}{3} \) = 40 days
    As 1 days work = \( \frac{1}{60} \) and Bs 1
    days work = \( \frac{1}{40} \)
    (A + B)s 1 days work
    = \( \frac{1}{60} \)+\( \frac{1}{40} \) = \( \frac{2+3}{120} \) = \( \frac{5}{120} \) = \( \frac{1}{24} \)
    Hence, both will finish the work in 24 days.





Ans .

(2) 25 days


  1. Explanation :

    (2) As 1 days work
    = (B +C)s 1 days work ...(i)
    (A + B)s 1 days work = \( \frac{1}{10} \)
    Cs 1 days work = \( \frac{1}{50} \)
    (A + B + C)s 1 days work
    = \( \frac{1}{10} \)+\( \frac{1}{50} \) = \( \frac{5+1}{50} \) = \( \frac{6}{50} \) = \( \frac{3}{25} \) ...(iii)
    (A + A)s 1 days work = \( \frac{3}{25} \)
    (By (i) & (iii)
    As 1 days work = \( \frac{3}{50} \)
    Bs 1 days work = \( \frac{1}{10} \)-\( \frac{3}{50} \)
    = \( \frac{5-3}{50} \) = \( \frac{2}{50} \) = \( \frac{1}{25} \)
    Hence, B alone will complete the
    work in 25 days





Ans .

(3) 7\( \frac{1}{2} \) days


  1. Explanation :

    (3) Using Rule 2,
    Let the son take x days to do the
    work.
    \( \frac{1}{5} \)+\( \frac{1}{x} \) = \( \frac{1}{3} \)
    => \( \frac{x+5}{5x} \) = \( \frac{1}{2} \)
    => 3x + 15 = 5x
    => 2x = 15 => x = \( \frac{15}{2} \) = 7\( \frac{1}{2} \) days





Ans .

(4) 40


  1. Explanation :

    (4) Let the number of men in the
    beginning = x
    Then, \( \frac{x+8}{x} \) = \( \frac{60}{50} \)
    => \( \frac{x+8}{x} \) = \( \frac{6}{5} \)
    => 6x = 5x + 40 => x = 40





Ans .

(1) 192


  1. Explanation :

    (1) 12 persons can complete a
    work in 4 days.
    => 24 persons can complete the work in 2 days.
    => 24 persons can complete the 8 times work in 16 days
    => 24*8 persons = 192 persons can complete the 8 times work in 2 days.





Ans .

(2) 110


  1. Explanation :

    (2) Let the original number of
    workers = x. Then,
    x*100 = (x -10)*110
    => 10x = 11x - 110
    => x = 110





Ans .

(3) 12 days


  1. Explanation :

    (3) Work done by 12 men in 6
    days = \( \frac{1}{2} \)
    Remaining work
    = 1-\( \frac{1}{2} \) = \( \frac{1}{2} \)
    6 men leave the work.
    Time taken = \( \frac{12*12}{6*2} \) = 12 days





Ans .

(2) 15


  1. Explanation :

    (2) Using Rule 1,
    60 men can complete a work in
    250 days.
    Work done by 60 men in 1 day
    = \( \frac{1}{250} \)
    => Work done by 60 men in 200
    days = \( \frac{200}{250} \) = \( \frac{4}{5} \)
    Remaining work = 1-\( \frac{4}{5} \) = \( \frac{1}{5} \)
    Work is stopped for 10 days.





Ans .

(1) 3 days


  1. Explanation :

    (1) Using Rule 2,
    Working 5 hours a day, A can complete a work in 8 days.
    i.e. A can complete the work in 40 hours.
    Similarly, B will complete the same work in 60 hours.
    (A + B)s 1 hours work
    = \( \frac{1}{40} \)+\( \frac{1}{60} \) = \( \frac{3+2}{120} \)
    = \( \frac{5}{120} \) = \( \frac{1}{24} \)
    Hence, A and B together will complete the work in 24 hours.
    They can complete the work in 3 days working 8 hours a day.





Ans .

(4) 2 days


  1. Explanation :

    (4) According to the question,
    2 persons with equal abilities can do 1 job in 1 day
    Time taken by 1 man to complete 1 job = 2 days
    => Time taken by 100 persons in completing 100 jobs = 2 days





Ans .

(2) 6.30 p.m.


  1. Explanation :

    (2) Part of the field mowed by
    Ganga and Saraswati in first 2
    hours
    = \( \frac{1}{8} \)+\( \frac{1}{12} \) = \( \frac{3+2}{24} \) = \( \frac{5}{24} \)
    Part of the field mowed in first
    8 hours = \( \frac{5*4}{24} \) = \( \frac{20}{24} \) = \( \frac{5}{6} \)
    Remaining work = 1 -\( \frac{5}{6} \) = \( \frac{1}{6} \)
    Now, it is the turn of Ganga, part
    of work done by Ganga in 1 hour = \( \frac{1}{8} \)
    Remaining work = \( \frac{1}{6} \)-\( \frac{1}{8} \) = \( \frac{1}{24} \)
    Now, time taken by Saraswati in
    completing this part of work
    = \( \frac{1}{24} \)*12 = \( \frac{1}{2} \) hour
    Total time = 9*\( \frac{1}{2} \) hour
    The mowing starts at 9 am.
    Hence, the mowing will be completed
    at 6.30 pm.





Ans .

(3) 200


  1. Explanation :

    (3) Using Rule 1,
    Remaining work
    = 5-\( \frac{7}{2} \) = \( \frac{3}{2} \)
    M1D1W2 = M2D2W1
    => 280*80*\( \frac{3}{2} \) = M2*20*\( \frac{7}{2} \)
    => M2 = \( \frac{280*80*30}{20*7} \) = 480
    Required number of additionalmen = 480 - 280 = 200





Ans .

(1) 6 days


  1. Explanation :

    (1) Let B alone do the work in x
    days.
    6*\( \frac{1}{12} \) + 3*\( \frac{1}{x} \) = 1
    => \( \frac{1}{2} \)+\( \frac{3}{x} \) = 1
    \( \frac{3}{x} \) = \( \frac{1}{2} \) => x = 6 days





Ans .

(4) 4:3


  1. Explanation :

    (4) Using Rule 15,
    Efficiency and time taken are inversely
    proportional.
    Required ratio = 4:3





Ans .

(3) 75


  1. Explanation :

    (3) Scheduled time to complete the
    work = 40 days
    25 men in 24 days do \( \frac{1}{3} \) work
    1 man in 1 day does \( \frac{1}{3*25*24} \) = \( \frac{1}{1800} \) work
    Work remaining = 1-\( \frac{1}{3} \) = \( \frac{2}{3} \)
    The work is to be completed 4
    days before schedule i.e.,
    in (40 - 4) = 36 days
    No. of days left for \( \frac{2}{3} \)rd work
    = 36 - 24 = 12 days
    \( \frac{1}{1800} \) work is done in 1 day by
    1 man.
    \( \frac{2}{3} \)rd work will be done in 12 days
    by
    1800*\( \frac{2}{3} \)*\( \frac{1}{12} \) = 100 men
    25 men are already working
    Extra men to be employed
    = 100 - 25 = 75





Ans .

(2) 4:3


  1. Explanation :

    (2) 20*16 women
    = 16*15 men
    => 4 women = 3 men
    => \( \frac{men}{women} \) = \( \frac{4}{3} \)
    Hence, working capacity of man :
    woman = 4:3





Ans .

(1) 45 days


  1. Explanation :

    (1) Man : Woman (efficiency)
    = 3:2
    i.e., Woman completes \( \frac{2}{5} \)
    th work in 18 days.
    Time taken by the woman to
    complete the whole work = \( \frac{18*5}{2} \) = 45 days





Ans .

(1) 3y:2x


  1. Explanation :

    (1) 1 mans 1 days work = \( \frac{1}{2x} \)
    1 womans 1 days work = \( \frac{1}{3y} \)
    Required ratio = \( \frac{1}{2x} \) \( \frac{1}{3y} \)
    = 3y:2x





Ans .

(2) 9 hrs


  1. Explanation :

    (2) Using Rule 1,
    D1T1 = DT2
    => 18*6 = 12*T2
    => T2 = \( \frac{18*6}{12} \) = 9 hrs





Ans .

(3) 138


  1. Explanation :

    (3) Using Rule 1,

    => 12*6*240*x = 18*8*36*460
    => x = \( \frac{18*8*36*460}{12*6*240} \) = 138





Ans .

(3) 30


  1. Explanation :

    (3) Using Rule 1,

    => 18*2*12*6*8x = 32*3*9*9*10*8
    => x = \( \frac{32*3*9*9*10*8}{18*2*12*6*8} \) = 30 days





Ans .

(2) 10


  1. Explanation :

    (2) (P + Q)s 1 days work = \( \frac{1}{6} \)
    (Q + R)s 1 days work = \( \frac{7}{60} \)
    Let P alone do the work in x
    days.
    According to the question,
    \( \frac{3}{x} \)+\( \frac{6*7}{60} \) = 1
    => \( \frac{3}{x} \) = 1-\( \frac{7}{10} \) = \( \frac{3}{10} \)
    => x = 10 days
    Qs 1 days work = \( \frac{1}{6} \)-\( \frac{1}{10} \) = \( \frac{1}{15} \)
    Rs 1 days work = \( \frac{7}{60} \)-\( \frac{1}{15} \) = \( \frac{1}{20} \)
    Time taken by R = 20 days
    Required answer = 20 - 10
    = 10 days





Ans .

(3) 25


  1. Explanation :

    (3) Let 150 workers complete the
    work in x days.
    150*x = 150 + 146 + .... to (x + 8) terms
    On putting x = 17
    LHS = 150*17 = 2550
    RHS = 150 + 146 + .... to 25 terms
    a = 150, d = - 4, n = 25
    S = \( \frac{n}{2} \)*[2a+(n-1)d]
    = \( \frac{25}{2} \)*[2*150 + 24*(-4)]
    = \( \frac{25}{2} \)*(300-96) = 2550
    Note : It is better to solve by options.





Ans .

(1) 20


  1. Explanation :

    (1) Using Rule 1,
    According to the question,
    M1D1 = M2D2
    =>(x + 4)*(x + 5)
    = (x - 5)*(x + 20)
    => x2 + 5x + 4x + 20
    = x2 - 5x + 20x - 100
    => 9x + 20 = 15x - 100
    => 15x - 9x = 100 + 20
    => 6x = 120 => x = 20





Ans .

(3) 10 days


  1. Explanation :

    (3) Let the work be finished in x
    days.
    \( \frac{x}{50} \)+\( \frac{x-1}{50} \)+\( \frac{x-2}{50} \)+ ... + \( \frac{1}{50} \) = 1
    => x + x - 1 + x - 2 + .... + 1 = 50
    i.e., 10 + 9 + 8 + .... + 1
    = 55
    9 + 8 + .... + 1 = 45
    Required time = 10 days





Ans .

(3) 10


  1. Explanation :

    (3)

    => 48*7*x = 20*21*8
    => x = \( \frac{20*21*8}{48*7} \) => x = 10





Ans .

(2) 6\( \frac{10}{33} \) days


  1. Explanation :

    (2) Area of the four walls and ceiling
    of the room
    = 2h (l + b) + lb
    = 2*10 (25 + 12) + 25*12
    = (20*37 + 300) sq. metre
    = (740 + 300) sq. metre
    = 1040 sq. metre
    Area painted by A in 1 day
    = \( \frac{250}{2} \) = 125 sq. metre
    Area painted by both in1 day
    = (125 + 40) sq. metre
    = 165 sq. metre
    Required time = \( \frac{1040}{165} \) = \( \frac{208}{33} \) = 6\( \frac{10}{33} \) days





Ans .

(1) 54


  1. Explanation :

    (1) Here, the length of wall is
    same in both cases.
    M1D1 = M2D2
    => 36*21 = M2*14
    => M2 = \( \frac{36*21}{14} \) = 54 days





Ans .

(2) 488 kg.


  1. Explanation :

    (2) Number of days in April and
    May = 30 + 31 = 61
    Q Requirement of rice for 7 days = 56 kg.
    Requirement of rice for 61 days
    = \( \frac{56}{7} \)*61 = 488 kg.





Ans .

(1) 40 minutes


  1. Explanation :

    (1) Total working time of school
    = (45*8) minutes
    = 360 minutes
    If 9 periods are held per day,
    Working time of each period
    \( \frac{360}{9} \) = 40 minutes





Ans .

(3) 7


  1. Explanation :





Ans .

(2) 45.


  1. Explanation :



TEST YOURSELF



Ans .

(2) 7\( \frac{1}{7} \)days


  1. Explanation :





Ans .

(4) 8 days


  1. Explanation :





Ans .

(2)120 days


  1. Explanation :

    (2) According to the question Work done by A and B together in one day =\( \frac{1}{10} \) part
    Work done by B and C together





Ans .

(1)42


  1. Explanation :

    (1) Using Rule 1,





Ans .

(2)RS.163.04


  1. Explanation :

    (2) Using Rule 1,
    Amount received by Meeta =\( \frac{6}{23} \)*625 = Rs. 163.04





Ans .

(1)35


  1. Explanation :





Ans .

(1)4 \( \frac{4}{5} \)day


  1. Explanation :

    (1) A`s one days work =\( \frac{1}{12} \)
    B`s one days work =\( \frac{1}{8} \)
    (A + B)s one days work=\( \frac{1}{12} \)+\( \frac{1}{8} \) =\( \frac{2+3}{24} \) =\( \frac{5}{24} \)
    Now,\( \frac{5}{24} \) work is done in 1day
    1 work is done in = \( \frac{24}{5} \)days =4 \( \frac{4}{5} \) days.





Ans .

(2)9 days


  1. Explanation :





Ans .

(3)12 days


  1. Explanation :





Ans .

(4)30 days


  1. Explanation :






Ans .

(1)36 days


  1. Explanation :





Ans .

(2)15 days


  1. Explanation :





Ans .

(3)3\( \frac{1}{3} \) days


  1. Explanation :






Ans .

(4)9 days


  1. Explanation :






Ans .

(1)40 days


  1. Explanation :






Ans .

(2)24 days


  1. Explanation :





Ans .

(3)18 days


  1. Explanation :





Ans .

(4)15 days


  1. Explanation :






Ans .

(1)20 days


  1. Explanation :






Ans .

(2)16.5 days


  1. Explanation :





Ans .

(3)240 days


  1. Explanation :