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    Due to 10% reduction in the price of sugar a person can buy 5 kg more sugar for ₹ 300. Find the reduced price of sugar per kg.
    Question

    Due to 10% reduction in the price of sugar a person can buy 5 kg more sugar for ₹ 300. Find the reduced price of sugar per kg.

    A.

    Rs. 6.00

    B.

    Rs. 5.75

    C.

    Rs. 6.50

    D.

    Rs. 5.25

    Correct option is A

    Given:

    Reduction in price = 10%

    Increased quantity = 5 kg

    Total money spent = ₹300

    Solution:

    Let the original price of sugar be ₹x per kg.
    Then, the quantity of sugar bought at the original price:​300x\frac{300}{x}

    After a 10% reduction, the new price per kg:​90100×x=910x\frac{90}{100} \times x = \frac{9}{10}x

    The new quantity of sugar bought = 300×109x\frac{300 \times 10}{9x}​​

    30009x300x=5\frac{3000}{9x} - \frac{300}{x} = 5

    30009x27009x=53009x=5300=5×9x300=45xx=30045=203\frac{3000}{9x} - \frac{2700}{9x} = 5\\\frac{300}{9x} = 5\\300 = 5 \times 9x\\300 = 45x\\x = \frac{300}{45} = \frac{20}{3}\\

    Reduced Price =  910x=910×203=6\frac{9}{10}x = \frac{9}{10} \times \frac {20}3 = 6 
    Alternate Solution:

    Price 1Consumption\propto \frac 1{\text{Consumption}}

    10% = 110\frac{1}{10}

    Price                                10      :          9

    Consumption                   9          :         10 

    1 unit = 5 kg  
    So, Final Purchase Quantity = R. 50 per kg

    Final price = 30050\frac{300}{50} = 6 


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