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Comparing Quantities Test - 43

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Comparing Quantities Test - 43
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  • Question 1
    1 / -0
    A shopkeeper buys an article at $$70\%$$ of its printed price. He spends $$Rs.\ 40$$ on transportation of the article. After charging Sales Tax at the rate of $$10\%$$ on the printed price, he sells the article for $$Rs.\ 7,040.$$ Find his profit as a percent to the nearest integer.
    Solution
    Let the printed price of the article be $$x.$$

    Then according to the statement,
    $$x+10\%$$ of $$x=7040$$
    $$\Rightarrow \dfrac{10x+x}{10}=7040$$
    $$\Rightarrow \dfrac{11x}{10}=7040$$
    $$\Rightarrow x=\dfrac{70400}{11}$$
    $$\Rightarrow x=Rs.\ 6400$$

    $$\therefore$$ Printed price of the article is equal to $$Rs.\ 6400.$$

    As given shopkeeper buys the article at $$70\%$$ of its printed price.
    For shopkeeper $$CP$$ of the article $$=70\%$$ of $$6400$$
                                                              $$=\dfrac{70}{100}\times 6400$$
                                                              $$=Rs.\ 4480$$

    Since he spend $$Rs.\ 40$$ on the transportation of the article, 
    Total cost price $$=4480+40$$
                               $$=Rs.\ 4520$$


    $$\text{Profit}=6400-4520$$
                  $$=Rs.\ 1880$$

    $$\text{Profit}\ \%=\dfrac{1880}{4520}\times 100$$
                       $$=41.59\%$$
                       $$\approx42\%$$
  • Question 2
    1 / -0
    Two merchants sell, each an article for Rs. $$1000$$. If merchant $$A$$ computes his profit on cost price, while merchant $$B$$ computes his profit on selling price, they end up making profits of $$25\%$$. By how much is the profit made by Merchant $$B$$ greater than that of Merchant $$A$$?
    Solution
    Merchant $$B$$ computes his profit as a percentage of selling price. He makes a profit of $$25\%$$ on selling price of Rs. $$1000$$ i.e. his profit $$=25\%$$ of $$1000=$$ Rs. $$250$$.
    Merchant $$A$$ computes his profit as a percentage of cost price.
    Therefore, when he makes a profit of $$25\%$$ or $$\left (\dfrac{1 }{4}\right)^{th}$$ of his cost price, then his profit expressed as a percentage of selling price $$=$$ or $$20\%$$ of selling price.
    So, merchant $$A$$ makes a profit of $$20\%$$ of Rs. $$1000=$$ Rs. $$200$$.
    Merchant B makes a profit of Rs. $$250$$ and merchant A makes a profit of Rs. $$200$$.
    Hence, merchant $$B$$ makes Rs. $$50$$ more profit than merchant $$A$$.
  • Question 3
    1 / -0
    A man buys an article for Rs. $$27.50$$ and sells it for Rs. $$28.60$$. Find his gain percent.
    Solution
    Given, selling price Rs. $$28.60$$ and cost price $$=27.50$$
    Gain $$=SP - CP $$
    $$=$$ Rs. $$ \begin{pmatrix}28.60 - 27.50\end{pmatrix}$$
    $$=$$ Rs. $$1.10$$
    Gain $$\%=\begin{Bmatrix}\begin{pmatrix}\dfrac{1.10}{27.50}\end{pmatrix}\times100\end{Bmatrix}\%=4\%$$
  • Question 4
    1 / -0
    If the cost price is $$96\%$$ of the selling price, then what is profit percent?
    Solution
    Let selling price be $$100$$,  then cost price will be $$96$$.

    Thus, profit $$=S.P-C.P=4$$

    Profit $$\%=\dfrac{\text {profit}}{\text{cost price}}\times 100 = \begin{pmatrix}\dfrac{4}{96}\end{pmatrix}\times100=4.17\%$$
  • Question 5
    1 / -0
    By selling a jeans for Rs. $$432$$, John loses $$4\%$$. For how much should John sell it to gain $$6\%$$?
    Solution
    SP of the shirt $$=432$$
    Loss $$=4\%$$
    Therefore, $$CP$$ of the shirt $$=\dfrac {100}{100-\text{loss} \%}\times SP$$
    $$=\dfrac {100}{100-4}\times 432$$
    $$=450$$
    Now,$$CP=450$$, desired gain $$=6\%$$
    Desired$$,SP=\dfrac {100+\text{gain} \%}{100}\times CP$$
                           $$=\dfrac {100+6}{100}\times 450$$
                           $$=477$$
    Hence, the desired selling price is Rs. $$477$$.
  • Question 6
    1 / -0
    A merchant marks his goods in such a way that the profit on sale of $$50$$ articles is equal to the selling price of $$25$$ articles. What is his profit margin ?
    Solution
    Let the selling price per article be $$=$$ Rs. $$1$$
    Therefore, selling price of $$50$$ articles $$=$$ Rs. $$50$$
    Profit on sale of $$50$$ articles $$=$$ selling price of $$25$$ articles $$=$$ Rs. $$25$$.
    S.P $$=$$Rs. $$ 50$$, Profit $$=$$ Rs. $$25$$ 
    Therefore, CP $$=$$ Rs.$$(50-25)=$$ Rs. $$25$$
    Profit $$\%=\dfrac{25}{25}\times100\%=100\%$$
  • Question 7
    1 / -0
    The cost of an article is decreased by $$15$$ $$\%$$. If the original cost is Rs. $$80$$, find the new cost.
    Solution
    Original cost of an article $$=$$ Rs. $$80$$
    Decrease in cost is $$=15$$ $$\%$$ of Rs. $$80=\dfrac{15}{100}\times80=\dfrac{1200}{100}=$$ Rs. $$12$$
    Therefore, new cost of an article $$=$$ Rs. $$80-$$ Rs. $$12=$$ Rs. $$68$$.
  • Question 8
    1 / -0
    The ratio in which tea costing Rs. $$192$$ per kg is to be mixed with tea costing Rs. $$150$$ per kg, so that the mixed tea when sold for Rs. $$194.40$$ per kg, gives a profit of $$20 \%$$
    Solution
    C.P of first tea $$=$$ Rs. $$192$$ per kg
    C.P of second tea $$=$$ Rs. $$150$$ per kg
    S.P of the mixture $$=$$ Rs. $$194.40$$ per kg.
    Profit $$=20\%$$
    Let C.P of the mixture be Rs. $$x$$ per kg
    $$\Rightarrow x+20$$% of $$x$$ $$=194.40$$
    $$\Rightarrow \dfrac{6x}{5}=194.40$$
    $$\Rightarrow 6x=194.40\times 5$$
    $$\Rightarrow x=\cfrac{972}{6}$$
    $$\Rightarrow x=$$ Rs. $$162$$ per kg
    Let $$N$$ kg is the first tea and $$N$$ kg is the second tea
    Then using Alligation, we have 
    First Tea $$=162-150=12$$
    Second tea $$=192-162=30$$
    $$\Rightarrow \dfrac{M}{N}=\dfrac{12}{30}$$
    $$\Rightarrow N:M=2:5$$
  • Question 9
    1 / -0
    The price of a TV is Rs. $$13,000$$. The sales tax  on it is $$12\%$$. Find the amount that Vinod will have to pay if he buys it.
    Solution
    Sales tax $$=$$ Price $$\times$$ Tax Rate
    $$=\dfrac{12}{100} \times 13000=1560$$
    Final price $$=13000+1560=14560$$
    Therefore, the amount that Vinod will have to pay will be Rs. $$14560$$.
  • Question 10
    1 / -0
    A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?
    Solution
    $$\Rightarrow$$  Let number of towels bought for $$\$120$$ be $$n$$.

    $$\Rightarrow$$  So price of single towel $$=\$\dfrac{120}{n}$$

    $$\Rightarrow$$  Now price of $$1$$ towel increases by $$\$1$$

    $$\Rightarrow$$  So, new price of single towel $$=\$\dfrac{120}{n}+1$$

    $$\Rightarrow$$  Number of towel that could be bought at this price = $$n-10$$

    $$\Rightarrow$$  So, new price of single towel = $$\dfrac{120}{(n-10)}$$

     So, by equating both new price of single towel,

    $$\Rightarrow$$  $$\dfrac{120}{n}+1=\dfrac{120}{(n-10)}$$

    $$\Rightarrow$$  $$\dfrac{(120+n)}{n}=\dfrac{120}{(n-10)}$$

    $$\Rightarrow$$  $$n^2-10n-1200=0$$

    $$\Rightarrow$$  $$(n-40)(n+30)=0$$

    $$\Rightarrow$$  $$n=40$$ or $$n=-30$$

    $$\Rightarrow$$   Number of towels is $$40$$.

    $$\Rightarrow$$   Current price per towel = $$\dfrac{120}{40}=\$\,3$$ 
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