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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 $$1$$st April.
    If $$1$$st is a Monday, then April will contain $$5$$ Mondays. This contradicts the given condition. Hence, $$1$$st April is not a Monday.
    Similarly, $$2$$nd April cannot be a Monday.
    So, $$3$$rd April is a Monday which satisfies the condition of $$4$$ Mondays in April. Hence, there will be $$4$$ Fridays in April (i.e. $$7, 14, 21, 28$$)
    Therefore, $$1$$st April is a Saturday.
  • Question 2
    1 / -0
    $$36$$  workmen are employed to finish a certain work in  $$48$$  days but it is found that in  $$24$$  days , only $$\dfrac{2}{5}$$ work is done. How many more men must be taken to finish the work in time?
    Solution
    $$\cfrac{2}{5} =\cfrac {(2 \times 100)}{ 5} = 40 \% $$ work completed in  $$24 $$ days
    so, $$60 \%$$  more is required to complete in  $$24$$ days
    If $$36$$  worker works for rest  $$48$$  days then work will be $$80 \% $$completed.
    To complete  $$20\ % $$ more work within the time they need  $$18$$  workers more.
  • Question 3
    1 / -0
    A train leaves from a station and moves at a certain speed. After $$2$$ hours, another train leaves from the same station and moves in the same direction at a speed of $$60$$ mph. If it catches up with the first train in $$ 4 $$ 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

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

    $$\Rightarrow V=40$$ $$mph$$
  • Question 4
    1 / -0
    $$2$$  men and $$5$$  women can do $$\dfrac{1}{4}$$th  of a job in  $$3 $$days . After  $$3$$  days ,  $$1 $$ man joined team and they completed another$$\dfrac{ 1}{4}$$ th of the job in $$ 2$$ days . How many men can complete the job in  $$4$$ 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  $$10$$  days. All the three started working at it together and after  $$4$$  days A left. Then B and C together completed the work in  $$10$$  more days. A alone could complete the work in :
    Solution

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

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

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

    $$\because \cfrac{3}{5}$$part of the work done by (B+C)= $$10$$ days 

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

    $$\therefore$$A alone work$$=\cfrac{1}{10}-\cfrac{3}{50}=\cfrac{1}{25}$$

    Hence A alone complete the work in $$25$$ days.



     

  • Question 6
    1 / -0
    A pump can fill a tank with water in  $$2$$  hours. Because of a leak in the tank, it take $$\dfrac{7}{3}$$ hours to fill the tank. The leak can empty the filled tank in:
    Solution
    Work done by pump in $$1$$ hr$$=\frac{1}{2}$$
    But because of leak work done by pump in $$1$$ hr $$\frac{3}{7}$$
    $$\therefore $$Work done by leak in $$1$$ hr=$$\frac{1}{2}-\frac{3}{7}=\frac{1}{14}$$
    Hence the leak can empty the filled tank in  $$14$$  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 $$3$$ oil filters or $$16$$ spark plugs per hour. At the end of the $$6$$ hour day, the company needs to have made  $$60$$  oil filters and  $$256$$ spark plugs. How many workers does the company need to employ to meet their quota ?
    Solution

    Work rate of workers = $$3$$ oil filters or $$16$$ spark plugs per hour.

    One worker works for $$6$$ hour,

    $$\therefore$$ Work = $$6\times3 = 18$$ oil filters or $$16\times6 = 96$$ Spark plugs

    If $$3$$ workers work on filters for $$6$$ hour, then they can make = $$18*3 = 54$$ oil filters.

    It means $$4th$$ worker needs $$2$$ more hours to complete $$60$$ oil filters.
    On other hand,

     $$2$$ workers can make $$96\times2 = 192$$ spark plugs
    Rest Spark =$$ 256 - 192 = 64$$.
    It means $$3rd$$ worker needs $$4$$ hours to complete $$64$$ spark plugs.

    $$\therefore$$ Total workers =$$ 3 +2 +1 = 6$$
    The $$6th$$ 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  $$16$$  min and another empty it in $$8$$ 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$$=\frac{1}{16}$$
    Waste tap empty  the  tank $$=\frac{1}{8}$$
    If both are open then work done by both in 1 min$$=\frac{1}{8}-\frac{1}{16}=\frac{1}{16}$$
    Now full tank will be emptied by them in $$16 $$ min
    Then half  tank will be emptied by them in  $$8$$  min

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