Question

A shopkeeper earns a profit of 10% on selling a book at 15% discount on the marked price. The ratio of the cost price to the marked price of the book is
A. \[112:17\]
B. \[17:22\]
C. \[112:85\]
D. None of these

Answer 1

Hint: In these types of questions take the initial price as Rs. 100 or in this case we can imagine that the printed price is Rs. 100. And then gain the rest of the numbers as we want the cost price, sell price and others.

Complete step by step answer:
Let the printed price be Rs. 100
Now we are given that the shopkeeper is selling a book at 15% discount on the marked price
Which makes the sell price \[100 - 15 = 85\] which is Rs. 85
Now we are also given that he is gaining a profit of 10%
So from here we can see that the cost price will become \[C.P. = \dfrac{{M.P.}}{{Gain + M.P.}} \times S.P.\]
So from here we first need to find \[{Gain + M.P.}\] Which will be \[100 + 10 = 110\]It must be noted that M.P. is referred to marked price C.P. is referred to Cost Price and S.P. is referred to Sell Price.
Now putting everything in the given formula we will be getting
\[\begin{array}{l}
C.P. = \dfrac{{100}}{{110}} \times 85\\
 = Rs.\dfrac{{8500}}{{110}}\\
 = Rs.\dfrac{{850}}{{11}}
\end{array}\]
Now the ratio C.P. : Printed Price
\[\begin{array}{l}
 = \dfrac{{850}}{{11}}:100\\
 = \dfrac{85}{{110}}\\
 = 17:22
\end{array}\]

So, the correct answer is “Option B”.

Note: It should be noted that, if cost price is denoted as CP and sale price as SP then \[loss = SP - CP\] and \[profit = CP - SP\] Which only makes sense because in loss CP > SP and in profit SP > CP.
Alternative: We can find cost price using value of profit percentage and selling price.