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Numerical Applications Test 23

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Numerical Applications Test 23
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  • Question 1
    1 / -0
    $$15$$ men can build a wall in $$60$$ days. How many more men are required to build another wall of same size in $$45$$ days?
    Solution
    Let $$x$$ men are required to build the wall in $$45$$ days.
    Then $$x:15::60:45$$
    $$\Rightarrow 45x=15\times 60$$
    $$\Rightarrow x=\dfrac{15\times 60}{45}$$
    $$x=20$$ men.
    Hence, $$20-15=5 $$ more men are required.
  • Question 2
    1 / -0
    A and B together can do a piece of work in $$ 6\dfrac{2}{3} $$ days , but B alone can do it in $$10$$ days. How long will A take to do it alone ?
    Solution
    A and B together can do a piece of work in $$ 6 \dfrac{2}{3}\left(\dfrac{20}{3}\right)$$ days
    (A+B)'s $$1$$ day's work$$=\dfrac{3}{20}$$

    B's $$1$$ day's work$$=\dfrac{1}{10}$$

    A's $$1$$ day's work$$=\dfrac{3}{20}-\dfrac{1}{10}=\dfrac{1}{20}$$.

    Hence, A can finish the work in $$20$$ days .

  • Question 3
    1 / -0
    Shrikant reads the following number of pages of a book daily. Find the mean.
    $$34, 43, 29, 51, 36, 41, 38, 35, 34, 36, 34, 38, 40, 36, 35,$$ 
    $$35, 34, 35, 36, 34, 38, 38, 35, 36, 34, 38, 36, 34, 35, 36 $$
    Solution
    The data numbers are: $$34, 43, 29, 51, 36, 41, 38, 35, 34, 36, 34, 38, 40, 36, 35, 35, 34, 35, 36, 34, 38, 38, 35, 36, 34, 38, 36, 34, 35, 36$$
    Mean = $$\cfrac{\text{Sum}}{\text{Total Numbers}}$$
    Sum of Numbers $$= 34 + 43 + 29 + 51 + 36 + 41 + 38 + 35 + 34 + 36 + 34 + 38 + 40 + 36 + 35 + 35$$ 
    $$+ 34 + 35 + 36 + 34 + 38 + 38 + 35 + 36 + 34 + 38 + 36 + 34 + 35 + 36$$
    Sum $$= 1094$$
    Total Numbers $$= 30$$
    Mean $$= \cfrac{1094}{30}$$
    Mean $$= 36.47$$
  • Question 4
    1 / -0
    The mean of $$3, a+ 2, 8, 12, 2a -1$$ and $$6$$ is $$7$$, find the value of $$a$$.
    Solution
    Given, mean is $$7$$.
    Therefore, mean $$=\dfrac {3+a+2+8+12+2a-1+6}{6}$$
    $$\Rightarrow 7=\dfrac {30+3a}{6}$$
    $$\Rightarrow 42=30+3a$$
    $$\Rightarrow 3a=12$$
    $$\Rightarrow a=4$$
  • Question 5
    1 / -0
    If $$10$$ horses consume $$18$$ bushels in $$36$$ days. How long will $$24$$ bushels last for $$30$$ horses?
  • Question 6
    1 / -0
    Twelve typists , all working with same speed type a certain number of pages in $$18$$ days working $$8$$ hours a day . How many hours per day must sixteen typists work in order to type the same number of pages in $$9$$ days?
    Solution
    $$\textbf{Step1-Find required working hour}$$
                  $$\text{Let the speed of typing of each typist $$=x$$ pages/hr}$$

                  $$\text{No of pages typed by $$12$$ typist in $$18$$ days working $$8$$ hrs a day}$$$$=8x\times 12\times 18$$

                                                                                                                                   $$=1728x$$ $$\text{pages}$$

                  $$\text{Working hrs required $$=1728$$ hrs}$$

                  $$\text{So hrs per day for $$16$$ persons in $$9$$ days }$$$$=\dfrac{1728}{9} \times 16$$

                                                                                          $$=12\text{ hrs/day}$$

    $$\textbf{Hence option C is correct}$$
  • Question 7
    1 / -0
    $$X$$ can do a piece of work in  $$24$$ days, while $$Y$$ alone can do it in $$16$$  days. With the help of $$Z$$ they finish the work in $$8$$ days.
    Find in how many days $$Z$$ can do the work alone?
    Solution
    $$X + Y + Z = \displaystyle\frac{1}{8}$$
    $$Z = \displaystyle\frac{1}{8} - X - Y$$
        $$= \displaystyle\frac{1}{8} - \displaystyle\frac{1}{24} - \displaystyle\frac{1}{16}$$
        $$ = \displaystyle\frac{1}{48}$$ 
    $$\therefore  Z$$ can do the work in 48 days.
  • Question 8
    1 / -0
    The mean monthly salary of the $$12$$ employees of a firm is Rs. $$1450$$. If one more person joins the firm who gets Rs. $$1645$$ per month, what will be the mean monthly salary of $$13$$ employees?
    Solution
    Mean salary of $$12$$ employees $$=$$ Rs. $$1450$$
    Sum of salary of $$12$$ employees $$= 12\times 1450 =$$ Rs. $$17400$$
    A new employee joins the firm and he gets, Rs $$1645$$
    Hence, new sum of salary $$= 17400 + 1645 = 19045$$
    New mean $$= \dfrac{19045}{13} = 1465$$
    The new mean salary of all the employees is Rs. $$1465$$
  • Question 9
    1 / -0
    $$12$$ men can complete a piece of work in $$16$$ days. How many days will $$4$$ men take to complete the task?
    Solution
    $$1$$ man will complete the job in $$16\times 12$$ days.
    So, $$4$$ will do in $$\displaystyle\frac{12\times 16}{4}=48$$ days.
    Hence, option $$D$$ is the correct answer.
  • Question 10
    1 / -0
    $$16$$ men can complete a piece of work in $$8$$ days. In how many days can $$12$$ men complete the same piece of work?
    Solution
    $$16$$ men can complete a piece of work in $$8$$ days
    $$\therefore\,1$$ man can complete the work in $$(16\times8)$$ days (Less men more days so multiply)
    $$\therefore\,12$$ men can complete the work in $$\displaystyle\frac{(16\times8)}{12}$$ days (More men less days, so divide)
    $$=\displaystyle\frac{32}{3}$$ days $$=10\displaystyle\frac{2}{3} $$ days.
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