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Numerical Applications Test 40

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Numerical Applications Test 40
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  • Question 1
    1 / -0
    Ram can do a price of work in $$6$$ days and Shyam can finish the same work in $$12$$ days. How much work will be finished if both work together for $$2$$ days?
    Solution
    Since, Ram can do a piece of work in $$6$$ days

    Therefore, One day's work of Ram $$= \dfrac {1}{6}$$

    Shyam can finish the same work in $$12$$ days

    Therefore One day's work of Shyam $$= \dfrac {1}{12}$$

    Hence, one day's work of them, if they work together

    $$\dfrac { 1 }{ 6 } +\dfrac { 1 }{ 12 } =\dfrac { 2 }{ 12 } +\dfrac { 1 }{ 12 } =\dfrac { 3 }{ 12 } =\dfrac { 1 }{ 4 } $$

    Therefore, two days' work of them is:

    $$\dfrac { 1 }{ 4 } \times 2=\dfrac { 1 }{ 2 } $$

    Hence, if they work together for $$2$$ days, then half of the work will be finished.
  • Question 2
    1 / -0
    A can do a piece of work in $$6\dfrac {2}{3}$$ days and B in $$5$$ days. They work together for $$2$$ days and then A leaves B to finish the work alone. How long will B take to finish it?
    Solution

  • Question 3
    1 / -0
    $$1200$$ men in a fort have provisions for $$28$$ days. After $$4$$ days, $$300$$ men leave the fort. How long will food last now?
    Solution
    Given that fort had provision of food for $$1200$$ men for $$28$$ days.

    Therefore, after $$4$$ days, the remaining food is sufficient for $$1200$$ men for $$24$$ days

    Remaining men after $$4$$ days $$= 1200 - 300 = 900$$

    Assume that after $$4$$ days,the remaining food is sufficient for $$900$$ men for $$x$$ days

    Now, we find for how long food lasts for $$900$$ men is as follows:

    $$\dfrac { 1200 }{ 900 } =\dfrac { x }{ 24 } \\ \Rightarrow x=\dfrac { 1200 }{ 900 } \times 24\\ \Rightarrow x=\dfrac { 4 }{ 3 } \times 24\\ \Rightarrow x=4\times 8\\ \Rightarrow x=32$$

    Hence, the food lasts for $$32$$ days now.
  • Question 4
    1 / -0
    In how many ways $$7$$ men and $$7$$ women can be seated around a round table such that no two women can sit together?
    Solution
    Lets first place the men (M). * here indicates the linker of round table *M -M - M - M - M* which is in $$(7-1)!$$ ways = $$6!$$
    So we have to place the women in between the men which is on the $$5$$ empty seats So $$7$$ women can sit on $$7$$ seats in $$(7)!$$ ways
    So the answer is $$7!\times 6!$$
  • Question 5
    1 / -0
    A can copy $$75$$ pages in $$25$$ hours, A and B together copy $$135$$ pages in $$27$$ hours. In what time can B copy $$42$$ pages?
    Solution

  • Question 6
    1 / -0
    Two pipes $$A$$ and $$B$$ can fill a cistern in $$37\displaystyle\frac{1}{2}$$ minutes and $$45\ minutes $$ respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the $$B$$ is turned off after :
    Solution
    Let B be turned off after x minutes. Then,
    Part filled by $$(A+B)$$ in x min. $$+$$ Part filled by A in $$(30-x)$$min. $$=1$$.
    $$\therefore x\left(\displaystyle\frac{2}{75}+\dfrac{1}{45}\right)+(30-x).\displaystyle\dfrac{2}{75}=1$$
    $$\Rightarrow \displaystyle\dfrac{11x}{225}+\dfrac{(60-2x)}{75}=1$$
    $$\Rightarrow 11x+180-6x=225$$.
    $$\Rightarrow x=9$$.
  • Question 7
    1 / -0
    A pump can fill a tank with water in $$2\ hours$$. Because of a leak, it took $$2\displaystyle\frac{1}{3}\ hours$$ to fill the tank. The leak can drain all the water of the tank in.
    Solution
    Rate of filling the Tank by Pump : $$\dfrac{1}{2} $$
    Rate of leak while water is being pumped in the tank: $$\dfrac{3}{7}$$

    Rate of leak in the tank: $$1$$ hour $$=\left(\displaystyle\frac{1}{2}-\frac{3}{7}\right)=\displaystyle\frac{1}{14}$$.
    $$\therefore$$ Leak will empty the tank in $$14$$ hrs.
  • Question 8
    1 / -0
    Which of the following is correct?
    Solution
    By numbering position we are actually fixing staring point which makes it similar to linear permutation.so option A is correct
    Linear permutation already has a staring point so it dose not need seats to be numbered   so option B is correct
  • Question 9
    1 / -0
    Two pipes P and Q would fill a cistern in $$24$$ and $$32$$ minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the cistern may be just filled in $$16$$ minutes
    Solution

  • Question 10
    1 / -0
    A cistern has a leak which would empty it in $$8$$ hours. A tap is turned on which admits $$6$$ litres a minute into the cistern and is now emptied in $$12$$ hours. How many litres does the cistern hold?
    Solution

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