• # How to solve this Profit and Loss question

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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?

• 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.

• 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)

Beware! I question everything and everybody.

• 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.

• 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

• 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