MathematicsA man sold a chair and a table together for Rs.1520 thereby making a profit of 25% on the chair and 10% on the table. By selling them together for Rs.1535 he would have made a profit of 10% on the chair and 25% on the table. Find the cost price of each

A man sold a chair and a table together for Rs.1520 thereby making a profit of 25% on the chair and 10% on the table. By selling them together for Rs.1535 he would have made a profit of 10% on the chair and 25% on the table. Find the cost price of each


  1. A
    C.P. of chair=Rs.800, C.P. of table=Rs.500
  2. B
    C.P. of chair=Rs.600, C.P. of table=Rs.700
  3. C
    C.P. of chair=Rs.800, C.P. of table=Rs.700
  4. D
    C.P. of chair=Rs.600, C.P. of table=Rs.500 

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    Solution:

    Concept: In order to solve the given question, first we will assume 2 variables for the cost price of each. Finding relation between two variables using condition 1. Similarly from the second condition you have 2 equations of 2 variables. So, apply a substitution method to solve and get the required answer.
    Here,
    cost of 1 chair= x and cost of one table= y
    profit on chair=25% then SP of chair= x+25100x
    =100x+25x100=54x.
    profit on table=10% then SP of table= y+10100y
    100y+10y100=1110y.
    54x+1110y=1520
    25x+22y=30400..1
    Now,
    profit on chair=10% then SP= x+10100x=100x+10x100=1110x
    profit on table=25% then SP of table= y+25100y=100y+25y100=54y
    1110x+54y=1535
    22x+25y=307002
    Now, substrate equation (2) from(1) we will get,
    3x-3y= -300
    x-y=-100.3
    Now Add equation (2) and (1) , we will get,
    47x+47y=61100
    x+y=13004
    Then solve equation ( 3) and (4) ,
     x-y= -100
    x+y=1300
    =>2x=1200
    x=600
    Now putting The value of x in equation (3)
    600-y= -100
    -y=-700
    y=700
    Therefore,
    CP of chair= Rs. 600 and CP of table= Rs. 700
    Hence, the correct option is 2.
     
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