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Comparing Quantities Test - 29

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Comparing Quantities Test - 29
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  • Question 1
    1 / -0
    A shopkeeper marks his goods $$20$$ $$\%$$ higher-than the cost price and allows a discount of $$5$$ $$\%$$. What is the percentage of his profit?
    Solution

    Let the C.P. of the article $$=$$ Rs. $$100$$. 
    Then, M.P. of the article$$ = $$ Rs. $$100 + $$ Rs. $$20 =$$ Rs. $$120$$
    Rate of Discount $$= 5\%$$
    $$\therefore $$ Discount offered $$= 5\% $$ of M.P. $$=\dfrac {5}{100}\times$$ Rs. $$120=$$ Rs. $$6$$
    $$\therefore $$ S.P. $$=$$ M.P. $$-$$ Discount $$=$$ Rs. $$120 - $$ Rs. $$6 =$$ Rs. $$114$$

    $$\text {Profit} =$$ S.P. $$-$$ CP. $$ =$$ Rs. $$114 -$$ Rs. $$100 =$$ Rs. $$14$$
    Profit $$\%=$$ $$\dfrac {14}{100}\times100 $$= $$14 \%$$

  • Question 2
    1 / -0
    A shopkeeper earns $$15$$% profit on a shirt even after allowing $$31$$% discount on the list price. If the list price is Rs. $$125$$, then what is the cost price of the shirt?
    Solution
    Discount on the shirt $$=31\%$$ of Rs. $$125$$
    $$=$$ Rs. $$\dfrac {31}{100}\times 125$$
    $$=$$ Rs. $$\dfrac {155}{4}$$
    Therefore, S.P. of the shirt $$=125-\dfrac {155}{4}$$
    $$=$$ Rs. $$\dfrac {345}{4}$$
    Therefore, C.P. of the shirt $$=\dfrac {345}{4}\times \dfrac {100}{115}$$
    $$=$$ Rs. $$75$$
    Thus, the cost price of the shirt is Rs. $$75$$.
  • Question 3
    1 / -0
    Find the rate of discount when M.P. $$=$$ Rs. $$975$$ and S.P. $$=$$ Rs. $$650$$.
    Solution
    Discount $$=$$ M.P. $$-$$ S.P. 
    $$=$$ Rs. $$975 -$$ Rs. $$650 =$$ Rs. $$325$$
    $$\therefore $$ Discount $$\% =$$ $$\left ( \dfrac {\text{Discount }}{\text{M.P.}}\times 100 \right )\%$$
    $$=\left ( \dfrac {325}{975}\times 100 \right )\%$$
    $$=\dfrac {100}{3}$$ $$\%=$$ $$33\dfrac {1}{3}\%$$
  • Question 4
    1 / -0
    A man sold a watch for Rs. $$600$$ at a loss. Had he sold if for Rs. $$750$$, his gain would have been double the former loss. The cost price of the watch is.
    Solution
    Let the cost price of watch is Rs. $$x$$
    Then loss $$=$$ Rs. $$x-600$$
    If watch sold Rs. $$750$$, then profit $$=$$ Rs. $$750-x$$ 
    Given gain has been double the loss 
    Then $$750-x=2(x-600)$$
    $$\Rightarrow 750-x=2x-1200$$
    $$\Rightarrow x=650$$
    Therefore, the cost price of the watch is Rs. $$650$$.
  • Question 5
    1 / -0
    Find the S.P. of a TV set whose marked price is Rs. $$17940$$ and the discount offered on it is $$8\%$$?
    Solution

    Given, M.P. $$=$$ Rs. $$17940$$, Discount $$=8\%$$

    S.P. $$=$$ M.P. $$-$$ Discount

    S.P $$=17940-8\%$$ of M.P.

    $$\Rightarrow 17940-\dfrac{8}{100}\times 17940$$

    $$\Rightarrow 17940-1435.20=$$ Rs. $$16504.80$$

  • Question 6
    1 / -0
    The rate of discount when M.P. $$=$$ Rs. $$ 4500$$  and S.P. $$=$$ Rs. $$4320$$
    Solution
    Given, M.P. $$=$$ Rs. $$4500$$ and S.P. $$=$$ Rs. $$4320$$
    $$\text{Rate of discount =} \dfrac{MP-SP}{MP}\times100$$
    $$=\dfrac{4500-4320}{4500}\times100$$
    $$=\dfrac{180}{4500}\times100$$
    $$=4\%$$
    Hence, option C is correct.
  • Question 7
    1 / -0
    The marked price of a pen is Rs. $$60$$.After allowing a discount of $$10 \%$$, the merchant makes a profit of $$20 \%$$. What is the cost price of the pen?
    Solution
    Let the cost price of a pen Rs. $$100$$
    The marchant make profit $$20\%$$, then selling price $$=$$ Rs. $$100+20=120$$
    Marked price Rs. $$60$$. Allowing discount $$10\%$$ then selling price $$=$$ $$\dfrac{60\times 90}{100}=54$$ Rs
    So, cost price $$=$$ $$\dfrac{54\times 100}{120}=$$ Rs. $$45$$
  • Question 8
    1 / -0
    The ratio between the sale price and cost price of an article is $$7: 5$$. What is the ratio between the profit and the cost price of that article ?
    Solution
    The ratio between the sale price and cost price of an article is $$7x: 5x.$$
    Then the profit becomes $$7x - 5x$$ which is $$2x$$.
    So, the ratio between profit and cost price is $$2x : 5x $$ or $$2 : 5$$.
  • Question 9
    1 / -0
    Find the marked price of a pair of shoes which are sold at $$Rs\ 2176$$ after allowing an off season discount of $$15 \% $$on them?
    Solution
    Let the market cost of pair of shoes is Rs $$100$$
    Then selling price after discount $$15$$%=$$100-15=85$$ Rs
    But he sell it Rs $$2176$$
    Then market price=$$\dfrac{2176\times 100}{85}=$$ Rs $$ 2560$$
  • Question 10
    1 / -0
    Find the amount actually paid for a mobile phone whose marked price is Rs. $$6600$$ and discount offered on it is $$12$$%.
    Solution
    Money discounted$$=12\% $$ of $$6600$$
                                   $$=6600\times\dfrac{12}{100}$$
                                   $$=792$$
    Actual amount $$=6600-792=5808$$
    Option D is correct.
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