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    How to solve this Profit and Loss question


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    Please solve this problem:
    Vijay bought some pens for Rs.540. He lost 2 pens on his way back to the shop. Then, he sold the rest of the pens at Rs.6 per pen more than what he gave for them. On the whole transaction, Vijay gained 10% on his outlay. How many pens did Vijay buy?
  • #144787

    This can be solved by solving a quadratic equation as follows -
    Let he bought n pens.
    So cost of 1 pen is 540/n
    He sold (n-2) pens at (540/n+6)
    His profit is ((n-2)*(540/n+6))-540
    Now devide it by cost and multiply by 100 to get profit in %
    Equate it to 10, you will get a quadratic equation n^2-11n-180=0
    Solve it with usual school method you will get n=20

    So he bought 20 pens


    Thoughts exchanged is knowledge gained.

  • #144789
    Let Vijay purchased x no. of pens. Each pen costs Rs. y
    As per the given conditions,
    xy=540................................(Equation no. 1)
    (x-2)(y+6)=540+54..........(Equation No. 2)
    xy+6x-2y-12=594
    Replacing xy by 540 and solving the equation, we get,
    x2-11x-180=0
    (x-20) (x+9)=180
    Therefore, x=20 (x=-9 to be ignored because the value of x can't be negative in this case)
    So, Vijay purchased 20 pens at the cost of Rs. 27 (Rs. 540/20) each.(Answer)

    Caution: Explosive. Handle with care.

  • #144802
    Let us assume that he purchased p number of pens.
    As he lost 2 pens on the way he sold the remaining (p-2) at a price 540/p+6 each.
    So profit = ((p-2)*(540/p+6))-540

    Now this profit can be converted to percentage by dividing by cost and multiplying by 100
    This percentage is given in the question as equal to 10 so we can solve this equality and get the equation p^2-11p-180=0 which on solving gives number of pens p=20 and purchase price =540/20=×27

    Knowledge is power.

  • #144809
    Let us say that he purchased N pens at rate of Rs,M/ per pen MXN=540
    He sold N-2 pens at the rate of M+6 per per. So total cost of sales is (N-2) (M+6) = 540+54
    This is Equal to NM-2M + 6N -12 = 594 . NM=MN=540. then the equation will be 540-2M+6N-12 =594 or it can be written as 540-2(540/N) +6N -12 -594=0 or 540-1080/N+6N-12-594=0 or 6N^2 -66N-1080=0 or N^2-11N-180=0 or (N+9)(N-20) =0 so the N value will be 20 . It indicates that he has purchased 20 pens.

    drrao
    always confident

  • #144846

    Cost price of some pens = Rs 540
    Suppose total no of pens that vijay buy = x
    Let cost of pen =y
    No of pens lost = 2
    Now total no of pens that vijay have = x-2
    Total profit gained = 10%
    Selling price of x-2 pens is = Rs 540 + 10% of 540
    According to question
    xy = 540 equation 1
    (x-2)(y+6)= 594
    xy+ 6x -2y-12=594
    540+6x-2*540/x-12=594
    6x-1080/x=594-540+12
    6x*x-1080=66x
    x*x-11x-180=0
    (x+9)(x-20)=0
    Means x= -9 or x = 20
    X cannot be negative so it is 20
    Total no of pens bought is 20


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