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Numerical Applications Test 35

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Numerical Applications Test 35
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  • Question 1
    1 / -0
    If 1010 workers can do a work in 1515 hours then 3030 workers can do it in _____  hours
    Solution
    This question is based on Inverse proprtion
    According to the given conditions,
    No. of workers            Time taken
      1010                              1515 hours
       3030                               xx days
    By inversion proportion, 
    10×15=30×x10\times15 = 30\times x
    x=10×1530\therefore x = \dfrac{10\times15}{30}
    x=5\therefore x =5
    Answer is 55 hours
  • Question 2
    1 / -0
    Two pipes A and B can fill a tank in 2020 and 3030 minutes respectively. If both the pipes are used together, then how long it will take to fill the tank?
    Solution
    Part filled by A in 11 min =120=\dfrac{1}{20}
    Part filled by B in 11 min =130=\dfrac{1}{30}
    Part filled by (A+B)\begin{pmatrix}A+B\end{pmatrix} in 11 min =120+130=112=\dfrac{1}{20}+\dfrac{1}{30}=\dfrac{1}{12}
    So both pipes can fill the tank in 1212 mins.
  • Question 3
    1 / -0
    A tap A can fill a cistern in 44 hours and the tap B can empty the full cistern in 66 hours. If both the taps are opened together in the empty cistern, in how much time will the cistern be filled up?
    Solution
    Time taken by tap A to fill the cistern =4  hours=4\;hours.
    Work done by tap A in 11 hour =14=\dfrac{1}{4}
    Time taken by tap B to empty the full cistern =6  hours=6\;hours.
    Work done by tap B in 11 hour =16=-\dfrac{1}{6} (since, tap B empties the cistern).
    Work done by (A+B)\begin{pmatrix}A+B\end{pmatrix} in 11 hour 14116=3212=112\dfrac{1}{4}-\dfrac{1}{16}=\dfrac{3-2}{12}=\dfrac{1}{12} part of the tank is filled.
    Therefore, the tank will fill the cistern =12  hours=12\;hours.
  • Question 4
    1 / -0
    A and B together can complete a work in 44 days. A alone can finish the work in 1212 days, In how many days B alone can finish the work?
    Solution
    (A+B)\begin{pmatrix}A+B\end{pmatrix}"s 11 day work =14=\dfrac{1}{4}
    A"s 11 day work =112=\dfrac{1}{12}
    B"s 11 day work =[(14)(112)]=16=\begin{bmatrix}\begin{pmatrix}\dfrac{1}{4}\end{pmatrix}-\begin{pmatrix}\dfrac{1}{12}\end{pmatrix}\end{bmatrix}=\dfrac{1}{6}
    So, B can complete the work in 66 days
  • Question 5
    1 / -0
    A group of workers can do a piece of work in 2424 days. However as 77 of them were absent it took 3030 days to complete work. How many people actually worked on the job to complete it?
    Solution
    Let the original number of workers in the group be "x x"
    therefore, actual number of workers =x7=x-7.
    We know that the number of man hours required to do the job is the same in both the cases.
    Therefore, x(24)=(x7).30x\begin{pmatrix}24\end{pmatrix}=\begin{pmatrix}x-7\end{pmatrix}.30
    24x=30x210\Longrightarrow 24x=30x-210
    6x=210\Longrightarrow 6x=210
    x=35\Longrightarrow x=35.
    Therefore, the actual number of workers who worked to complete the job =x7=357=28=x-7=35-7=28.
  • Question 6
    1 / -0
    Pipe A can fill a tank in 55 hours, pipe B in 1010 hours and pipe C in 3030 hours. If all the pipes are open, in how many hours will the tank be filled?
    Solution
    Part filled by A in 11 hour =15=\dfrac{1}{5}
    Part filled by B in 11 hour =110=\dfrac{1}{10}
    Part filled by C in 11 hour =130=\dfrac{1}{30}
    Part filled by (A+B+C)\begin{pmatrix}A+B+C\end{pmatrix} in 11 hour =15+110+130=13=\dfrac{1}{5}+\dfrac{1}{10}+\dfrac{1}{30}=\dfrac{1}{3}
  • Question 7
    1 / -0
    If 1616 workers can do a work in 2020 hours then how many workers can do the work in 1010 hours?
    Solution
    This question is based on Inverse proprtion
    According to the given conditions,
    No. of workers                   Time taken
      1616                                       2020 hours
       xx                                        1010 hours
    By inversion proportion, 
    16×20=x×1016\times20 = x\times10
    x=16×2010\therefore x = \dfrac{16\times20}{10}
    x=32\therefore x =32
    Answer is 3232 workers
  • Question 8
    1 / -0
    33 pipes are required to fill a tank in 11 hour. How long it will take to fill a tank by 55 pipes?
    Solution
    This question is based on Inverse proprtion
    According to the given conditions,
    No. of pipes           Time taken
      33                              11 hours
       55                              xx hours
    By inversion proportion, 
    3×1=5×x3\times1 = 5\times x
    x=3×15\therefore x = \dfrac{3\times1}{5}
    x=0.6\therefore x = 0.6 hours
    x=0.6\therefore x = 0.6 hours×60\times60 minutes =36 = 36 minutes
    Answer is 3636 minutes
  • Question 9
    1 / -0
    1515 persons complete a work in 44 days by working 66 hours a day. How many days it will take to complete the work if 55 persons work same hours per day?
    Solution
    No of person is inversely proportional to the no of days.
    Again, no of hours is inversely proportional to the no of days.
    So, 15×4=k=5×x15\times 4 = k = 5\times x
    x=12\Rightarrow x = 12; taking no of hours per day constant.

  • Question 10
    1 / -0
    What is the proportionality between the production of cakes & days and production of cakes & hours respectively?
    Solution
    If no of days increase, no of cakes increase accordingly. Similarly, if no of hours increase, no of cakes increase accordingly.
    Hence, both are in direct proportions.
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