Question

By what percent above the cost price should a dealer mark a pen so that after allowing a discount of 4% he gains 20%?

Answer 1

Hint: This problem is somewhat tricky but we can easily solve this. We will consider the cost price of the pen as 100. Also we will assume the marked price to be x according to this we will try to find the marked price and then the percentage by which the dealer should mark the price to gain 20% profit.

Complete step by step solution:
Let the cost price of the pen is Rs.100
Now the gain given is 20%.
 \[gain = 20\% of100 = Rs.20\]
So \[S.P. = C.P. + gain = 100 + 20 = Rs.120\]
Now let the marked price be x.
Discount of 4% is given and we know that discount is given on market price.
So, discount = 4% of marked price
 \[discount = Rs.\dfrac{4}{{100}}x\]
 \[discount = Rs.\dfrac{1}{{25}}x\]
This is the discount.
We know that, S.P. is the difference between the marked price and discount.
That is,
S.P.=M.P.-discount
Assigning the values,
 \[S.P. = x - \dfrac{x}{{25}}\]
Taking the LCM on Right hand side,
 \[S.P. = \dfrac{{25x - x}}{{25}}\]
 \[S.P. = \dfrac{{24x}}{{25}}\]
But we have found that S.P. is Rs.120
So we can write,
 \[120 = \dfrac{{24x}}{{25}}\]
To find the value of x we will cross multiply the numbers,
 \[x = \dfrac{{120 \times 25}}{{24}}\]
On dividing by 24 we get,
 \[x = 5 \times 25 = Rs.125\]
This is the marked price.
The amount that is increased above the cost price is Rs.25
Now we have to find the percentage by which it is increased.
 \[{{\% increase = }}\dfrac{{{\text{amount increased}}}}{{{\text{C}}{\text{.P}}{\text{.}}}} \times 100\]
Substituting the values,
 \[{{\% increase = }}\dfrac{{{\text{25}}}}{{{\text{100}}}} \times 100\]
Cancelling 100,
 \[{{\% increase = 25\% }}\]
This is the complete solution.
So, the correct answer is “25%”.

Note: The way of solution mentioned above is quite easy. We can also solve this by considering the marked price be 100 but that would unreasonably complicate the problem. Only notifying things is consider the relations between the prices like selling price, cost price and marked price. Discount is given on marked price always. And after giving the discount the amount becomes the selling price.