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Numerical Applications Test 15

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Numerical Applications Test 15
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  • Question 1
    1 / -0
    The mean of a sample is:
    Solution
    $$Mean= \dfrac {Total\quad of\quad sample\quad values}{sample\quad size}$$
    Answer-Option $$D$$.
  • Question 2
    1 / -0
    Arithmetic mean of $$2$$ and $$8$$ is
    Solution


    $${\textbf{Step -1: Stating the arithmetic mean of n general numbers.}}$$

                     $${\text{Let there be }}n{\text{ numbers }}{a_1}{\text{,}}{a_2}{\text{,}}{a_3}.....{a_n}{\text{. }}$$

                     $${\text{Arithmetic mean of the numbers = }}\dfrac{{{a_1} + {a_2} + {a_3}{\text{ + }}.....{\text{ + }}{a_n}{\text{.}}}}{n}$$

    $${\textbf{Step -2: Finding arithmetic mean of 2 and 8.}}$$

                     $${\text{Here we have only two numbers -  }}2,8$$

                     $${\text{Arithematic mean }}A = \dfrac{{2 + 8}}{2} = \dfrac{{10}}{2} = 5$$

    $${\textbf{Hence, }}\ {\textbf{Arithematic mean of 8 annd 2 is 5.}}$$

  • Question 3
    1 / -0
    The monthly average expenditure of a family with $$4$$ members is Rs.$$2,800$$. Find the monthly average expenditure of a family with only $$3$$ members.
    Solution

    Here,

    Expenditure of $$4$$ members $$=Rs.\ 2800$$

    So, expenditure of $$1$$ member $$=\dfrac{2800}{4}=Rs.\ 700$$

     

    Therefore,

    Expenditure of $$3$$ members $$=700\times 3=Rs.\ 2100$$

     

    Hence, this is the required result.
  • Question 4
    1 / -0
    The basic unit of speed is:
    Solution
    We know that the basic unit of speed is
    $$=meter\ per\ second$$

    Hence, this is the answer.
  • Question 5
    1 / -0
    10 men can finish the construction of a hut in 8 days.How many men are needed to finish the same in half day?
    Solution
    Using $$M_1d_1=M_2d_2$$
    $$10 \times 8=x \times \dfrac{1}{2}$$
    $$x=160$$ men
  • Question 6
    1 / -0
    It takes 8 people working at equal rates to finish a work in 96 days. How long 6 workers take for the same work?
    Solution
    solution:
    8 people takes 96 days to complete a peice of work 
    1 people will take $${96 \times 8}$$ days to complete same peice of work

    6 people will take $$\dfrac{96 \times 8}{6}$$ days= 128 days 

    hence the correct answer : B
  • Question 7
    1 / -0
    The Bubna dam has four inlets.Through the first three inlets,the dam can be filled in 12 minutes; through the second, the third and the fourth inlet,it can be filled in 15 minutes; and through the first and the first inlet, in 20 minutes.How much time will take all the four inlets to fill up the dam?
    Solution
    Let Pipes be A,B ,C and D
    $$\dfrac{1}{A}+\dfrac{1}{B}+\dfrac{1}{C}=\dfrac{1}{12}$$
    $$\dfrac{1}{B}+\dfrac{1}{C}+\dfrac{1}{D}=\dfrac{1}{15}$$
    $$\dfrac{1}{A}+\dfrac{1}{D}=\dfrac{1}{20}$$
    Adding all equations
    $$2[\dfrac{1}{A}+\dfrac{1}{B}+\dfrac{1}{C}+\dfrac{1}{D}]=\dfrac{1}{12}+\dfrac{1}{15}+\dfrac{1}{20}=\dfrac{1}{5}$$
    $$\dfrac{1}{A}+\dfrac{1}{B}+\dfrac{1}{C}+\dfrac{1}{D}=\dfrac{1}{10}min$$
    All the inlets together can fill in 10 min
  • Question 8
    1 / -0
    Two taps 'A' and 'B' can fill a water reservoir in 8 and 6 hours respectively, A third tap 'C' can empty the tank completely in 24 hours.How long would it take to fill the empty tank when all the taps are open?
    Solution
    Tap A can fill in 8 hr. B in 6 hr, C can empty reservoir in 24 hr
    All 3 can fill reservoir in 1 hr
    $$=\dfrac{1}{8}+\dfrac{1}{6}-\dfrac{1}{24}=\dfrac{6+8-2}{48}=\dfrac{12}{48}$$

    All three can fill whole reservoir in $$\dfrac{48}{12}$$i.e. 4 hr.
  • Question 9
    1 / -0
    A tank can be filled up by two pipes A and B in $$2$$ hours and $$3$$ hours respectively.A third pipe C can empty the full tank in $$6$$ hours.If all the taps can be turned on at the same time, the tank will be full in 
    Solution
    Pipe A and B can fill tank in 2 and 3 hours respectively and C can empty in 6 hours.
    $$\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{6}=\dfrac{3+2-1}{6}$$
    $$=\dfrac{4}{6}=\dfrac{2}{3}$$
    i.e. the tank can be filled in $$\dfrac{3}{2}=1.5$$ hours.
  • Question 10
    1 / -0
    If the seventh day of a month is three days earlier than Fridays, what day will it be on the nineteenth day of the month?
    Solution
    $$7$$th day$$=$$ three days earlier than Friday.
    $$\Rightarrow 7$$th day $$=$$ Tuesday
    $$\Rightarrow 19$$th day$$=$$ Sunday.
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