Question

A man bought an article and sold it at a gain of 5% . If he had bought it at 5% less and sold it for Re.1 less he would have made a profit of 10%. The CP of the article was
A.200 Rs
B.300 Rs
C.400 Rs
D.500 Rs

Answer 1

Hint: Assuming the cost price to be x . we can calculate the selling price with the gain percent and cost price using $ \Rightarrow S.P = \left( {\dfrac{{100 + gain\% }}{{100}}} \right)*CP$. And in the next case the cost price is reduced by 5% of old cost price and using that we can find the new selling price and as the new selling price is Re.1 less than the old selling price the difference between them is Re.1 .solving for x we get the cost price.

Complete step-by-step answer:
Let the cost price of the article be x
In the first case we are given that the article was sold at a gain of 5%
When we are given the cost price and gain percent ,
$ \Rightarrow S.P = \left( {\dfrac{{100 + gain\% }}{{100}}} \right)*CP$
\[
   \Rightarrow S.P = \left( {\dfrac{{100 + 5}}{{100}}} \right)*x \\
   \Rightarrow S.P = \dfrac{{105x}}{{100}} \\
\]
Let this be equation (1)
Now in the second case we are given that if the cost price is reduced by 5%
That is ,
Cost price = old cost price – 5% of cost price
   $
   = x - \dfrac{5}{{100}}x \\
   = \dfrac{{100x - 5x}}{{100}} \\
   = \dfrac{{95x}}{{100}} \\
$
Same way in the second case we are given that if he buys the article at and sells it Re.1 less then he would have a profit of 10%
Then ,
New selling price = $\left( {\dfrac{{100 + gain\% }}{{100}}} \right)*CP$
\[
   \Rightarrow S.P = \left( {\dfrac{{100 + 10}}{{100}}} \right)*\dfrac{{95x}}{{100}} \\
   \Rightarrow S.P = \dfrac{{110}}{{100}}*\dfrac{{95x}}{{100}} = \dfrac{{209x}}{{200}} \\
\]
 As in the case we are selling the article Re . 1 less than the old selling price
Then the difference between the old selling price and new selling price is 1
$
   \Rightarrow \dfrac{{105x}}{{100}} - \dfrac{{209x}}{{200}} = 1 \\
   \Rightarrow \dfrac{{21000x - 20900x}}{{20000}} = 1 \\
   \Rightarrow 100x = 20000 \\
   \Rightarrow x = \dfrac{{20000}}{{100}} = 200 \\
$
Hence the cost price is Rs. 200
The correct option is a.

Note: There are many formulas to find the cost price according to the details given
Formula to calculate cost price if selling price and profit percentage are given:
$CP = \dfrac{{SP*100}}{{100 + profit\% }}$
Formula to calculate cost price if selling price and loss percentage are given:
$CP = \dfrac{{SP*100}}{{100 - loss\% }}$