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Comparing Quantities Test - 51

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Comparing Quantities Test - 51
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  • Question 1
    1 / -0
    A men's clothing retailer order $ $$25,400$$ worth of outer garments and receives a discount of $$15$$% followed by an additional discount of $$10$$%. What is the cost of the clothing after these two discounts?
    Solution
    First he got $$15$$ $$\%$$ discount, therefore after discount the cost of clothing is $$\left (1-\dfrac{15}{100}\right) \times 25400 = 21590$$
    Now he got additional $$10$$ $$\%$$ discount
    Now the cost of clothing is $$\left (1-\dfrac{10}{100}\right) \times 21590 = 19431$$
  • Question 2
    1 / -0
    The price of commodity $$X$$ increases by $$40$$ paise every year, while the price of commodity $$Y$$ increases by $$15$$ paise every year. If in $$2001$$, the price of commodity $$X$$ was Rs. $$4.20$$ and that of $$Y$$ was Rs. $$6.30$$, in which year commodity $$X$$ will cost $$40$$ paise more than the commodity $$Y$$?
    Solution
    Suppose commodity $$X$$ will cost $$40$$ paise more than $$Y$$ after $$z$$ years.

    Then, $$\left( 4.20+0.40z \right) -\left( 6.30+0.15z \right) =0.40$$

    $$\Rightarrow 0.25z=0.40+2.10$$

    $$\Rightarrow z=\dfrac { 2.50 }{ 0.25 } =\dfrac { 250 }{ 25 } =10$$.

    $$\therefore$$ $$X$$ will cost $$40$$ paise more than $$Y$$ $$10$$ years after $$2001 $$ which is  $$2011$$.
  • Question 3
    1 / -0
    If an item is purchased at $ $$150$$ and sold at $ $$165$$, what percent of the original cost is the profit?
    Solution
    Given:
    cost price$$=150$$ dollar
    Selling price$$=165$$ dollar
    Profit$$=$$selling price$$-$$cost price
    $$=165-150=15$$ dollar
    Percent of the original cost$$=\dfrac{15}{150}\times 100$$
    $$=10\%$$
    Option 'E'.
  • Question 4
    1 / -0
    Which set of the statement can give the percentage of discount given?
    I. $$23.5$$% profit was earned by selling an almirah for $$Rs. 12,350$$.
    II. If there were no discount, the earned profit would have been $$30$$%.
    III. The cost price of the almirah was $$Rs. 10,000$$.
    Solution
    $$(1)$$ $$S.P. = Rs. 12350, Gain = 23.5$$%

    $$\therefore C.P. = Rs. \left (\dfrac {100}{123.5}\times 12350\right ) = Rs. 10,000$$.

    $$(2)$$ $$M.P. = 130$$% of $$C.P. = 130$$% of $$Rs. 10,000 = Rs, 13,000$$.

    From $$(1)$$ and $$(2)$$, discount $$= Rs. (13000 - 12350) = Rs. 650$$.

    Discount % $$= \left (\dfrac {650}{13000}\times 100\right )$$% $$= 5$$%.

    Thus, $$(1)$$ and $$(2)$$ give the answer.

    $$(2)$$ and $$(3) $$ can not give the answer. Because we require profit percentage with discount and profit percentage without discount. So $$(2)$$ and $$(3)$$ are not sufficient to give the discount percentage.

    Also, $$(1)$$ and $$(3)$$ can not give the answer because C.P. can already be calculated with the use of $$(1)$$ statement only but we need the discount percentage.

    Since $$(3)$$ gives only $$ C.P. = Rs. 10,000$$, $$(1)$$ and $$(2)$$ give the answer.
    Therefore, $$(1)$$ and $$(2)$$ give the answer.

    $$\therefore$$ Correct answer is (A).
  • Question 5
    1 / -0
    The first year's interest on a sum of money lent at $$8$$% compound interest is $$Rs. 48$$. The second year's amount is
    Solution

  • Question 6
    1 / -0
    The calculation of interest on the interest of principal amount is called
    Solution
    The calculation of interest on the interest of principal amount is called $$Compound\,\,interest$$.
    Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. 
    It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
    Compound interest is standard in finance and economics.
  • Question 7
    1 / -0
    Anagha borrowed Rs.$$ 70,000$$ from her friend at the rate of $$3.5\%$$ p.a.compounded yearly. She returned the amount after three years. So calculate interest of first year and second year .
    Solution
    $$P=70000,R=3.5$$%
    Interest in $$1$$st year$$=\cfrac { P\times R\times T }{ 100 } $$
    $$=\cfrac { 70000\times 3.5\times 1 }{ 100 } $$
    $$=2450$$
    Now, $$(2450+P)$$ will be principal amount for $$2$$nd year since interest is compounded yearly
    Interest in $$2$$nd year$$=\cfrac { { P }^{ ' }\times R\times T }{ 100 } $$
    $$=\cfrac { (2450+70000)\times 3.5\times 1 }{ 100 } $$
    $$=724.5\times 3.5=2535.75$$
  • Question 8
    1 / -0
    Megha lended Rs.$$8000$$ as a loan for $$4$$ years at the rate $$4\%$$ compounded annualy. Calculate the interest she will recive by the method of simple interest.
    Solution
    $$P=8000,R=4$$%, $$T=4$$
    Interest in $$1$$st year$$=\cfrac { P\times R\times T }{ 100 } $$
    $$=\cfrac { 8000\times 4\times 1 }{ 100 } $$
    $$=320$$
    Now, Principal amount will be $$(P+320)$$ since the  interest in compounded annually.
    Interest in $$2$$nd year$$=\cfrac { { P }^{ ' }\times R\times T }{ 100 } $$
    $$=\cfrac { 8320\times 4\times 1 }{ 100 } $$
    $$=332.8$$
    Now, $$P''=332.8+P'$$
    Interest in $$3$$rd year$$=\cfrac { 8652.8\times 4\times 1 }{ 100 } =346.112$$
    Interest in $$4$$th year$$=\cfrac { (346.112+8652.8)\times 4\times 1 }{ 100 } =359.956$$
    Total interest$$=320+332.8+346.112+359.95$$
    $$=1358.86$$
  • Question 9
    1 / -0
    Ranjana borrowed the money Rs$$1,00,000$$ for $$3$$ years at the rate $$3.5\%$$ p.a. compounded annually. Calculate interest to be paid.
    Solution
    $$\Rightarrow$$  Here, Principal amount for first year = $$Rs.1,00,000$$
    $$\Rightarrow$$  First year Interest = $$\dfrac{100000\times 3.5}{100}=Rs.3500$$

    $$\Rightarrow$$  Principal amount for second year = $$Rs.1,00,000+Rs.3500=Rs.1,03,500.$$ 
    $$\Rightarrow$$  Second year interest = $$\dfrac{103500\times 3.5}{100}=Rs.3622.5$$

    $$\Rightarrow$$  Principal amount for third year = $$Rs.1,03,500+Rs.3622.5=Rs.1,07,122.5$$
    $$\Rightarrow$$  Third year interest = $$\dfrac{107122.5\times 3.5}{100}=Rs.3749.28$$

    $$\therefore$$  Total Interest = $$Rs.3500+Rs.3622.5+Rs.3749.28=Rs.10871.78$$
  • Question 10
    1 / -0
    An industrialist borrowed the $$Rs\ 75,000$$ for two years at the rate $$2.5\%$$ p.a.compounded annually. Calculate the total amount compound interest by simple interest method.
    Solution
    $$P=75000,R=2.5$$%, Time$$=2$$yrs

    Interest in $$1$$st year$$=\cfrac { P\times R\times T }{ 100 } $$

    $$=\cfrac { 75000\times 2.5\times 1 }{ 100 } $$

    $$=1875$$

    $$P'=(1875+P)$$

    Interest in $$2$$nd year$$=\cfrac { { P }^{ ' }\times R\times T }{ 100 } $$

    $$=\cfrac { 76875\times 2.5\times 1 }{ 100 } $$

    $$=1921.875$$

    Total interest$$=1875+1921.875$$

    $$=3796.875$$

    Total amount=Principal$$+$$Total interest

    $$=75000+3796.875$$

    $$=78796.875$$
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