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Numerical Applications Test 5

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Numerical Applications Test 5
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  • Question 1
    1 / -0
    X and Y together can do a piece of work in $$8$$ days, which X alone can do in $$12$$ days. In how many days can Y do the same work alone?
    Solution
    $$X$$'s one day's work $$ = \displaystyle\frac { 1 }{ 12 }$$

    Let, $$Y$$ work for $$x$$ days

    $$\therefore Y$$'s one day's work $$ = \displaystyle\frac { 1 }{ x }$$

    One day work by $$X$$ and $$Y$$ together

    $$\displaystyle {\frac{1}{12}\, +\, \frac{1}{x}\, =\, \frac{1}{8}}$$

    $$\displaystyle {\frac{1}{x}\, =\, \frac{1}{8}\, -\, \frac{1}{12}\, =\, \frac{1}{24}}$$

    $$\therefore$$ $$x = 24$$ days

    $$\therefore Y $$ can complete work alone in 24 days.
  • Question 2
    1 / -0
    The day after tomorrow will be X-mas day. What will be the day on New-year-day if today is Monday?
  • Question 3
    1 / -0
    In the series given below. count the number of 9s, each of which Is not immediately preceded by 5 but is immediately followed by either 2 or 3. How many such 9s are there?
    1 9 2 6 5 9 3 8 3 9 3 2 5 9 2 9 3 4 8 2 6 9 8
    Solution
    There are 3 such 9s that are not immediately preceded by 5 and immediately followed by 2 or 3 in the given series. They are marked in bold.
    1 9 2 6 5 9 3 8 3 9 3 2 5 9 2 9 3 4 8 2 6 9 8
    Answer is Option B
  • Question 4
    1 / -0
    A tank can be filled by one tap in 209 minutes and by another in 25 minutes. Both the taps are kept open for 5 minutes and then the second is turned off. In how many minutes more is the tank completely filled?
    Solution
    Let flow rate of first tank $$=xm^3/min$$. Flow rate of $$2^{nd}tap=ym^3/min$$.
    Let volume of tank $$=m^3$$
    $$20x=v$$
    $$x=\dfrac {v}{20}$$
    $$25y=v$$
    $$Y=\dfrac {v}{25}$$
    $$5t=\dfrac {v-5x-5y}{x}=11 min$$
  • Question 5
    1 / -0
    If the seventh day of a month is three days earlier than Friday, what day will it be on the nineteenth day of the month?
    Solution
    Seventh day of the month is three days earlier than Friday i.e. it is Tuesday.
    The fourteenth day will also be a Tuesday.
    Nineteenth day is five days ahead. 
    Therefore, nineteenth day will be a Sunday.
    Answer is Option A
  • Question 6
    1 / -0
    If 4th day of any month was Sunday, what will be the day on 27th day of the same month ?
  • Question 7
    1 / -0
    Find the arithmetic mean of $$24 $$ and $$36.$$
    Solution
    Arithmetic mean of two quantity $$a,b$$ $$= \dfrac{a+b}{2}$$

    $$AM $$ of $$24, 36 = \dfrac{24+36 }{2} = \dfrac{60}{2} = 30$$
  • Question 8
    1 / -0
    $$3$$ men of $$7$$ women can do a piece of work in $$32$$ days. The number of days required by $$7$$ men and $$5$$ women to do a piece of work twice as large is
    Solution
    Work of 3 men $$=$$ work of 7 women
    Work of 1 man $$=$$ work of $$\displaystyle\frac{7}{3}$$ women

    Work of 7 men $$=$$ work of $$\displaystyle\frac{7\times7}{3}$$

    $$\displaystyle=\frac{49}{3}$$ women

    $$\therefore$$ Work of 7 men + 5 women

    $$=$$ work of $$\displaystyle\frac{49}{3}+5$$

    $$\displaystyle=\frac{64}{3}$$ women

    $$\displaystyle\begin{matrix}Women&Days\\7&32\\\frac{64}{3}&x\end{matrix}$$

    $$\displaystyle\therefore\frac{64}{3}:7::32:x$$

    $$\displaystyle\therefore\frac{64}{3}\times x=7\times32$$

    $$\displaystyle\therefore x=\frac{7\times32\times3}{64}=10.5\:days$$

    $$\therefore$$ So, 7 men and 5 women can do piece of work twice as large in $$21$$ days.
  • 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
    $$\displaystyle Men\qquad Work$$
    $$\displaystyle 12\downarrow \qquad 16\uparrow $$
    $$\displaystyle 4\qquad \qquad x$$

    $$\displaystyle \therefore \dfrac { 12 }{ 4 } =\dfrac { x }{ 16 } $$

    $$\displaystyle \Rightarrow x=\dfrac { 12\times 16 }{ 4 } =48days$$
  • Question 10
    1 / -0

    Directions For Questions

    Mr and Mrs Aggarwal were married in November and their children Sahil and Sonia are November born too Sahil's birthday is celebrated 10 days before Sonia's birthday and 7 days after the marriage anniversary of parents The marriage anniversary of Mr. and Mrs. Agarawal was celebrated on second Sunday of the November month and last day of the month also happened to be Sunday

    ...view full instructions

    What is date of birth of Sahil?
    Solution
    30th November is Sunday. Second Sunday of November is 9th November. Sahil's birthday is 7 days after the anniversary of his parents. So his birthday falls on 16th November.
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