Question

A dealer allows a discount of Rs.10% and still gains by 10%. What should be the marked price if the cost price is Rs.900?

Answer 1

Hint: Assuming the marked price to be x. We know than when a A% discount is given it is nothing other than A% of the marked price and the selling price is given by subtracting the discount amount from the marked price.Then as the person gains 10% on selling the product it is given by 10% of the cost price and the other way to find gain is subtracting cost price from selling price and equating this gives us the value of x.

Complete step by step solution:
Now let the marked price be x
We are given that the product was sold with a discount of 10 %
Hence we know that
Discount = 10% of MP
$ \Rightarrow Discount = \dfrac{{10}}{{100}}\times x = \dfrac{x}{{10}}$
Whenever a discount a given our selling price is given by
$
   \Rightarrow SP = MP - Discount \\
   \Rightarrow SP = x - \dfrac{x}{{10}} \\
   \Rightarrow SP = \dfrac{{10x - x}}{{10}} = \dfrac{{9x}}{{10}} \\
 $
It is also given that the person gains 10% on selling the product
The gain is nothing other than 10% of the price with which he brought the product
$
   \Rightarrow Gain = 10\% {\text{ }}of{\text{ }}CP \\
   \Rightarrow Gain = \dfrac{{10}}{{100}}\times 900 = 90 \\
 $
Hence we get that the person gains Rs.90 on selling the product
We also know that
$ \Rightarrow Gain = SP - CP$
Using the known values we get
$
   \Rightarrow 90 = \dfrac{{9x}}{{10}} - 900 \\
   \Rightarrow 90 = \dfrac{{9x - 9000}}{{10}} \\
   \Rightarrow 900 = 9x - 9000 \\
   \Rightarrow 900 + 9000 = 9x \\
   \Rightarrow 9900 = 9x \\
   \Rightarrow \dfrac{{9900}}{9} = x \\
   \Rightarrow x = 1100 \\
 $
Now we get the value of x

And hence the marked price is Rs.1100

Note :
The problem can also be solved using another set of formulae
We have the discount to be 10% and gain to be 10%
And we have the cost price to be 900
Let the marked price be x
The formula to find the cost price is as follows
$ \Rightarrow CP = \dfrac{{100 - discount\% }}{{100 - gain\% }}\times MP$
Using the known values we get
$
   \Rightarrow 900 = \dfrac{{100 - 10}}{{100 + 10}}\times x \\
   \Rightarrow 900 = \dfrac{{90}}{{110}}\times x \\
   \Rightarrow 900\times \dfrac{{11}}{9} = x \\
   \Rightarrow 100\times 11 = x \\
   \Rightarrow x = 1100 \\
 $
Therefore the marked price is Rs.1100.