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Numerical Applications Test 34

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Numerical Applications Test 34
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  • Question 1
    1 / -0
    Mr. Leelanand Kumar looks at the calendar for 2012, He finds that April 2012 has exactly four Mondays  and four Fridays. 1st April 2012 would fall on ?
    Solution
    Let us start with 11st April.
    If 11st is a Monday, then April will contain 55 Mondays. This contradicts the given condition. Hence, 11st April is not a Monday.
    Similarly, 22nd April cannot be a Monday.
    So, 33rd April is a Monday which satisfies the condition of 44 Mondays in April. Hence, there will be 44 Fridays in April (i.e. 7,14,21,287, 14, 21, 28)
    Therefore, 11st April is a Saturday.
  • Question 2
    1 / -0
    3636  workmen are employed to finish a certain work in  4848  days but it is found that in  2424  days , only 25\dfrac{2}{5} work is done. How many more men must be taken to finish the work in time?
    Solution
    25=(2×100)5=40%\cfrac{2}{5} =\cfrac {(2 \times 100)}{ 5} = 40 \% work completed in  2424 days
    so, 60%60 \%  more is required to complete in  2424 days
    If 3636  worker works for rest  4848  days then work will be 80%80 \% completed.
    To complete  20 20\ % more work within the time they need  1818  workers more.
  • Question 3
    1 / -0
    A train leaves from a station and moves at a certain speed. After 22 hours, another train leaves from the same station and moves in the same direction at a speed of 6060 mph. If it catches up with the first train in 4 4 hours, what is the speed of the first train?
    Solution
    Distance traveled By First Train in 6 Hours = Distance traveled By Second Train in 4 Hours

    V(2+4)=60×4\Rightarrow V(2+4)=60\times 4
    V(6)=60×4\Rightarrow V(6)=60\times 4  

    V=40\Rightarrow V=40 mphmph
  • Question 4
    1 / -0
    22  men and 55  women can do 14\dfrac{1}{4}th  of a job in  33 days . After  33  days ,  11 man joined team and they completed another14\dfrac{ 1}{4} th of the job in 2 2 days . How many men can complete the job in  44 days ?
    Solution
    Work rate of Man and Women,
    (2/m) + (5/w) = 1/ (4 *3)..............(i)
    (3/m) + (5/w) = 1/ (4 *2)............(ii)
    (2) - (1)
    1/m = 1/24
    m = 24
    It means one man needs 24 days to complete the work so work completed in  4 days , we need 
    24/4 = 6 men.
  • Question 5
    1 / -0
    A , B and C together can complete a piece of work in  1010  days. All the three started working at it together and after  44  days A left. Then B and C together completed the work in  1010  more days. A alone could complete the work in :
    Solution

    (A+B+C)'s one days's work=110=\cfrac{1}{10}

    So (A+B+C)'s 4 day's work=410=25=\cfrac{4}{10}=\cfrac{2}{5}

    Remaining part of the work=125=35=1-\cfrac{2}{5}=\cfrac{3}{5}

    35\because \cfrac{3}{5}part of the work done by (B+C)= 1010 days 

    \therefore  1 work done by (B+C)=1035=503 Days=\cfrac{10}{\cfrac{3}{5}}=\cfrac{50}{3}  Days

    \thereforeA alone work=110350=125=\cfrac{1}{10}-\cfrac{3}{50}=\cfrac{1}{25}

    Hence A alone complete the work in 2525 days.



     

  • Question 6
    1 / -0
    A pump can fill a tank with water in  22  hours. Because of a leak in the tank, it take 73\dfrac{7}{3} hours to fill the tank. The leak can empty the filled tank in:
    Solution
    Work done by pump in 11 hr=12=\frac{1}{2}
    But because of leak work done by pump in 11 hr 37\frac{3}{7}
    \therefore Work done by leak in 11 hr=1237=114\frac{1}{2}-\frac{3}{7}=\frac{1}{14}
    Hence the leak can empty the filled tank in  1414  hours.
  • Question 7
    1 / -0
    A company makes car parts and has a certain quota to meet each day. Every worker in the company can turn out either 33 oil filters or 1616 spark plugs per hour. At the end of the 66 hour day, the company needs to have made  6060  oil filters and  256256 spark plugs. How many workers does the company need to employ to meet their quota ?
    Solution

    Work rate of workers = 33 oil filters or 1616 spark plugs per hour.

    One worker works for 66 hour,

    \therefore Work = 6×3=186\times3 = 18 oil filters or 16×6=9616\times6 = 96 Spark plugs

    If 33 workers work on filters for 66 hour, then they can make = 183=5418*3 = 54 oil filters.

    It means 4th4th worker needs 22 more hours to complete 6060 oil filters.
    On other hand,

     22 workers can make 96×2=19296\times2 = 192 spark plugs
    Rest Spark =256192=64 256 - 192 = 64.
    It means 3rd3rd worker needs 44 hours to complete 6464 spark plugs.

    \therefore Total workers =3+2+1=6 3 +2 +1 = 6
    The 6th6th worker will work on both filter making and as well as spark plugs.

    hence the answer is option B

  • Question 8
    1 / -0
    A tap can fill a tank in  1616  min and another empty it in 88 min. If the tank is already half full and both the taps are opened together, the tank will be
    Solution
    Tap fill the tank in 1 minute=116=\frac{1}{16}
    Waste tap empty  the  tank =18=\frac{1}{8}
    If both are open then work done by both in 1 min=18116=116=\frac{1}{8}-\frac{1}{16}=\frac{1}{16}
    Now full tank will be emptied by them in 1616 min
    Then half  tank will be emptied by them in  88  min

  • Question 9
    1 / -0
    66 oxen or 88 cows can gaze a field in 2828 days. How long would 99 oxen and 22 cows take to graze the same field?
    Solution
    66 oxen =8=8 cows
    11 oxen =86=\dfrac{8}{6} cows
    99 oxen =86×9=\dfrac{8}{6}\times9 cows =12=12 cows
    (9oxen+2cows)(12cows+2cows)=14cows\begin{pmatrix}9\text{oxen}+2\text{cows}\end{pmatrix}\equiv\begin{pmatrix}12\text{cows}+2\text{cows}\end{pmatrix}=14\text{cows}
    Now, 88 cows can graze the field in 2828 days
    11 cow can graze the field in (28×8)\begin{pmatrix}28\times8\end{pmatrix} days
    1414 cows can graze the field in 28×814\dfrac{28\times8}{14} days =16=16 days.
  • Question 10
    1 / -0
    66 typist working 55 hours a day can type the manuscript of a book in 1616 days. How many days will 44 typists take to do the same job, each working 66 hrs a day?
    Solution
    66 typists working 55 hours a day can finish the job in 1616 days
    66 typists working 11 hour a day can finish it in (16×5)\begin{pmatrix}16\times5\end{pmatrix} days
    11 typist working 11 hour a day can finish it in 16×5×66\dfrac{16\times5\times6}{6} days
    11 typist working 66 hours a day can finish it in 66 days
    44 typists working 66 hours a day can finish it 16×5×66×4\dfrac{16\times5\times6}{6\times4} days =20=20 days.
    Hence, 44 typists working 66 hours a day can finish the job in 2020 days.
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